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Papers by Kjell-Ove Widman

Research paper thumbnail of Asymptotic Behavior of Solutions of Parabolic Equations with Discontinuous Coefficients

Mathematica Scandinavica, Jun 1, 1970

Research paper thumbnail of Harmonic mappings into Riemannian manifolds with non-positive sectional curvature

MATHEMATICA SCANDINAVICA, 1975

Research paper thumbnail of La storia di Arne Beurling

matematica e cultura 2008

Uno dei risultati di maggior rilievo ottenuti dai servizi di intelligence durante la seconda guer... more Uno dei risultati di maggior rilievo ottenuti dai servizi di intelligence durante la seconda guerra mondiale fu la decodifica del piu complesso sistema di comunicazione crittografica in uso presso i tedeschi, il T52 Geheimschreiber, conosciuto anche come Sturgeon (Storione, Fig. 1). L’artefice di questa impresa fu Arne Beurling, un giovane professore svedese di matematica. Il suo successo fu reso ancora piu straordinario dal fatto che egli lavoro completamente da solo e partendo praticamente da zero, senza nessuna conoscenza iniziale dei metodi impiegati nei procedimenti di crittografIa. Eppure gli occorsero meno di tre settimane per comprendere il funzionamento del sistema e sviluppare un metodo di crittoanalisi. Grazie alla sua scoperta, le autorita svedesi furono in grado di decifrare e leggere circa 250.000 messaggi scambiati tra l’ambasciata tedesca e il ministero degli affari esteri a Berlino e tra il quartier generale tedesco a Berlino e le truppe tedesche in Norvegia e Finlandia.

Research paper thumbnail of Dirichlet's boundary value problem for harmonic mappings of Riemannian manifolds

Mathematische Zeitschrift, 1976

Research paper thumbnail of Some regularity results for quasilinear elliptic systems of second order

Mathematische Zeitschrift, 1975

Research paper thumbnail of Local bounds for solutions of higher order nonlinear elliptic partial differential equations

Mathematische Zeitschrift, 1971

Research paper thumbnail of H�lder continuity of solutions of elliptic systems

Manuscripta Mathematica, 1971

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Research paper thumbnail of On the hölder continuity of solutions of elliptic partial differential equations in two variables with coefficients inL∞

Communications on Pure and Applied Mathematics, 1969

Research paper thumbnail of A quantitative form of the maximum priniciple for elliptic partial differential equations with coefficients in L∞

Communications on Pure and Applied Mathematics, 1968

KJELL-OVE WIDMAN 51. We shall consider (weak) solutions of the equation in a bounded domain R c R... more KJELL-OVE WIDMAN 51. We shall consider (weak) solutions of the equation in a bounded domain R c R", n 5 2. The equation is supposed to satisfy aaj E L , , A, IEi2 5 ai*[Jj 5 AZ IEI2, a*j = aji. If R satisfies an internal sphere condition, we can prove THEOREM 1. Let u be a bounded solution of (1) in R, and let X , be any point in Q. Then to every y > 0 there exist constants K , = K,(Q, L, X , , u(X,)m) and K , = K,(Q, L, X , , Mu(X,)), where m = infn u, M = supn u, such that (2) u (X)-M I-Kz Sn"+"(X), (3) u(X)m 2 K ,-Sn'A+y(X) .

Research paper thumbnail of On the boundary behavior of solutions to a class of elliptic partial differential equations

Arkiv för Matematik, 1967

Research paper thumbnail of On the preceding paper by J�ger

Archive for Rational Mechanics and Analysis, 1970

Research paper thumbnail of On the boundary values of harmonic functions in R3

Arkiv för matematik, 1964

Research paper thumbnail of The Green function for uniformly elliptic equations

Manuscripta Mathematica, 1982

... For fixed x6 ~ we consider the function G(.) := G(x,- which is the Green function correspondi... more ... For fixed x6 ~ we consider the function G(.) := G(x,- which is the Green function corresponding to L t. We have to distinguish between four cases. ... GI8 ~ ~ O. As G(-) and Kix-yl2-nuR (-) are solutions E of Ltu=O in ~N(BR(Y~)~CR) and G~ Kix-yi2-nuR on the ...

Research paper thumbnail of An existence theorem for harmonic mappings of Riemannian manifolds

Research paper thumbnail of On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order

Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze, 1977

L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scien... more L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Research paper thumbnail of On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order

Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze, 1977

L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scien... more L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Research paper thumbnail of Invited Talk - Special Session on Arne Beurling: Arne Beurling: Mathematician and Code Breaker

Research paper thumbnail of Codebreakers: Arne Beurling and the Swedish Crypto Program During World War II

Part 1: An 18th century cipher The world's first ciphering machine Damm, Hagelin, and Gylden ... more Part 1: An 18th century cipher The world's first ciphering machine Damm, Hagelin, and Gylden Radio signal interception and cryptanalysis before 1939 War Enter Arne Beurling The Russian Baltic Navy Mysterious signals Teleprinters Beurling's Analysis The G-Schreiber and the apps Continued cryptanalysis Exit Gylden--but Beurling comes back The double transposition Operation Barbarossa The work place Contents The birth of the FRA Brilliant results--despite everything Downturn and leakage The Red Army and the Arctic Sea The doubly enciphered Russian code Stella Polaris Gradual loss of German traffic Borelius pays a visit to the Germans Information--but of what value? Norway The last years of the war The Swedes' own crypto systems Arne Beurling 1943-1945 Part 2: Arne Beurling Through the eyes of a woman A magical friendship Sources Index of names.

Research paper thumbnail of Littlewood-Paley a priori estimates for parabolic equations with sub-Dini continuous coefficients

L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scien... more L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Research paper thumbnail of Swedish Cryptology II

I n this second installment about Swedish cryptology, we will describe the successes and failures... more I n this second installment about Swedish cryptology, we will describe the successes and failures in intercepting, cryptanalyzing, and reading the secret messages of potentially hostile and other countries during WW2. The information gathered aided the government in its quest to stay neutral and kept the military leadership informed about possible threats of invasion.

Research paper thumbnail of Asymptotic Behavior of Solutions of Parabolic Equations with Discontinuous Coefficients

Mathematica Scandinavica, Jun 1, 1970

Research paper thumbnail of Harmonic mappings into Riemannian manifolds with non-positive sectional curvature

MATHEMATICA SCANDINAVICA, 1975

Research paper thumbnail of La storia di Arne Beurling

matematica e cultura 2008

Uno dei risultati di maggior rilievo ottenuti dai servizi di intelligence durante la seconda guer... more Uno dei risultati di maggior rilievo ottenuti dai servizi di intelligence durante la seconda guerra mondiale fu la decodifica del piu complesso sistema di comunicazione crittografica in uso presso i tedeschi, il T52 Geheimschreiber, conosciuto anche come Sturgeon (Storione, Fig. 1). L’artefice di questa impresa fu Arne Beurling, un giovane professore svedese di matematica. Il suo successo fu reso ancora piu straordinario dal fatto che egli lavoro completamente da solo e partendo praticamente da zero, senza nessuna conoscenza iniziale dei metodi impiegati nei procedimenti di crittografIa. Eppure gli occorsero meno di tre settimane per comprendere il funzionamento del sistema e sviluppare un metodo di crittoanalisi. Grazie alla sua scoperta, le autorita svedesi furono in grado di decifrare e leggere circa 250.000 messaggi scambiati tra l’ambasciata tedesca e il ministero degli affari esteri a Berlino e tra il quartier generale tedesco a Berlino e le truppe tedesche in Norvegia e Finlandia.

Research paper thumbnail of Dirichlet's boundary value problem for harmonic mappings of Riemannian manifolds

Mathematische Zeitschrift, 1976

Research paper thumbnail of Some regularity results for quasilinear elliptic systems of second order

Mathematische Zeitschrift, 1975

Research paper thumbnail of Local bounds for solutions of higher order nonlinear elliptic partial differential equations

Mathematische Zeitschrift, 1971

Research paper thumbnail of H�lder continuity of solutions of elliptic systems

Manuscripta Mathematica, 1971

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Research paper thumbnail of On the hölder continuity of solutions of elliptic partial differential equations in two variables with coefficients inL∞

Communications on Pure and Applied Mathematics, 1969

Research paper thumbnail of A quantitative form of the maximum priniciple for elliptic partial differential equations with coefficients in L∞

Communications on Pure and Applied Mathematics, 1968

KJELL-OVE WIDMAN 51. We shall consider (weak) solutions of the equation in a bounded domain R c R... more KJELL-OVE WIDMAN 51. We shall consider (weak) solutions of the equation in a bounded domain R c R", n 5 2. The equation is supposed to satisfy aaj E L , , A, IEi2 5 ai*[Jj 5 AZ IEI2, a*j = aji. If R satisfies an internal sphere condition, we can prove THEOREM 1. Let u be a bounded solution of (1) in R, and let X , be any point in Q. Then to every y > 0 there exist constants K , = K,(Q, L, X , , u(X,)m) and K , = K,(Q, L, X , , Mu(X,)), where m = infn u, M = supn u, such that (2) u (X)-M I-Kz Sn"+"(X), (3) u(X)m 2 K ,-Sn'A+y(X) .

Research paper thumbnail of On the boundary behavior of solutions to a class of elliptic partial differential equations

Arkiv för Matematik, 1967

Research paper thumbnail of On the preceding paper by J�ger

Archive for Rational Mechanics and Analysis, 1970

Research paper thumbnail of On the boundary values of harmonic functions in R3

Arkiv för matematik, 1964

Research paper thumbnail of The Green function for uniformly elliptic equations

Manuscripta Mathematica, 1982

... For fixed x6 ~ we consider the function G(.) := G(x,- which is the Green function correspondi... more ... For fixed x6 ~ we consider the function G(.) := G(x,- which is the Green function corresponding to L t. We have to distinguish between four cases. ... GI8 ~ ~ O. As G(-) and Kix-yl2-nuR (-) are solutions E of Ltu=O in ~N(BR(Y~)~CR) and G~ Kix-yi2-nuR on the ...

Research paper thumbnail of An existence theorem for harmonic mappings of Riemannian manifolds

Research paper thumbnail of On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order

Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze, 1977

L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scien... more L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Research paper thumbnail of On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order

Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze, 1977

L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scien... more L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Research paper thumbnail of Invited Talk - Special Session on Arne Beurling: Arne Beurling: Mathematician and Code Breaker

Research paper thumbnail of Codebreakers: Arne Beurling and the Swedish Crypto Program During World War II

Part 1: An 18th century cipher The world's first ciphering machine Damm, Hagelin, and Gylden ... more Part 1: An 18th century cipher The world's first ciphering machine Damm, Hagelin, and Gylden Radio signal interception and cryptanalysis before 1939 War Enter Arne Beurling The Russian Baltic Navy Mysterious signals Teleprinters Beurling's Analysis The G-Schreiber and the apps Continued cryptanalysis Exit Gylden--but Beurling comes back The double transposition Operation Barbarossa The work place Contents The birth of the FRA Brilliant results--despite everything Downturn and leakage The Red Army and the Arctic Sea The doubly enciphered Russian code Stella Polaris Gradual loss of German traffic Borelius pays a visit to the Germans Information--but of what value? Norway The last years of the war The Swedes' own crypto systems Arne Beurling 1943-1945 Part 2: Arne Beurling Through the eyes of a woman A magical friendship Sources Index of names.

Research paper thumbnail of Littlewood-Paley a priori estimates for parabolic equations with sub-Dini continuous coefficients

L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scien... more L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Research paper thumbnail of Swedish Cryptology II

I n this second installment about Swedish cryptology, we will describe the successes and failures... more I n this second installment about Swedish cryptology, we will describe the successes and failures in intercepting, cryptanalyzing, and reading the secret messages of potentially hostile and other countries during WW2. The information gathered aided the government in its quest to stay neutral and kept the military leadership informed about possible threats of invasion.