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Papers by Oldrich John

Research paper thumbnail of Gas exhalation and its calculations. I

Applications of Mathematics

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 some regularity and nonregularity results for solutions to parabolic systems

Research paper thumbnail of Some (new) counterexamples of parabolic systems

We give examples of parabolic systems (in space dimension n ≥ 3) having a solution with real anal... more We give examples of parabolic systems (in space dimension n ≥ 3) having a solution with real analytic initial and boundary values which develops the discontinuity in the interior of the parabolic cylinder.

Research paper thumbnail of Interior C 1, γ-Regularity for Weak Solutions of Nonlinear Second Order Parabolic Systems

Communications in Partial Differential Equations, Nov 22, 2011

Research paper thumbnail of Nowhere continuous solutions to elliptic systems

Commentationes Mathematicae Universitatis Carolinae

Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic 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 Function Spaces

Research paper thumbnail of Partial regularity for solutions of quasilinear parabolic systems with nonsmooth in time principal matrix

Nonlinear Analysis: Theory, Methods & Applications, 2014

Partial regularity for solutions of quasilinear parabolic systems with nonsmooth in time principa... more Partial regularity for solutions of quasilinear parabolic systems with nonsmooth in time principal matrix is proved in the paper. Only boundedness of this matrix is assumed in time variable. To prove the result, we apply the method of modified A-caloric approximation assuming that the matrix A is not the constant one but depends on the time variable t.

Research paper thumbnail of On the Hölder continuity of gradient of solutions to a class of elliptic systems

Functiones et Approximatio Commentarii Mathematici, 2009

The interior C 1,γ-regularity for weak solutions with BMO-gradient of nonlinear nonautonomous sec... more The interior C 1,γ-regularity for weak solutions with BMO-gradient of nonlinear nonautonomous second order systems satisfying Legendre-Hadamard ellipticity condition is investigated.

Research paper thumbnail of Interior C 1, γ -Regularity for Weak Solutions of Nonlinear Second Order Parabolic Systems

Communications in Partial Differential Equations, 2006

ABSTRACT The interior C -regularity for the first gradient with respect to the space variables of... more ABSTRACT The interior C -regularity for the first gradient with respect to the space variables of a weak solution to a class of nonlinear second order parabolic systems is proven under the assumption that oscillations of coefficients are controlled by the ellipticity constant.

Research paper thumbnail of Morrey space regularity for weak solutions of Stokes systems with VMO coefficients

Annali di Matematica Pura ed Applicata

We prove that for weak solutions (u, p) of Stokes system with symmetric elliptic coefficients mat... more We prove that for weak solutions (u, p) of Stokes system with symmetric elliptic coefficients matrix A whose entries are bounded and VMO functions and with right-hand side f in Morrey space L 2,μ their symmetric gradients Eu and p belong to the same Morrey space L 2,μ .

Research paper thumbnail of Remarks on C1,γ-Regularity of Weak Solutions to Elliptic Systems with BMO Gradients

Zeitschrift für Analysis und ihre Anwendungen, 2009

Research paper thumbnail of Function Spaces

Research paper thumbnail of Gas exhalation and its calculations. I

Applications of Mathematics

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 some regularity and nonregularity results for solutions to parabolic systems

Research paper thumbnail of Some (new) counterexamples of parabolic systems

We give examples of parabolic systems (in space dimension n ≥ 3) having a solution with real anal... more We give examples of parabolic systems (in space dimension n ≥ 3) having a solution with real analytic initial and boundary values which develops the discontinuity in the interior of the parabolic cylinder.

Research paper thumbnail of Interior C 1, γ-Regularity for Weak Solutions of Nonlinear Second Order Parabolic Systems

Communications in Partial Differential Equations, Nov 22, 2011

Research paper thumbnail of Nowhere continuous solutions to elliptic systems

Commentationes Mathematicae Universitatis Carolinae

Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic 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 Function Spaces

Research paper thumbnail of Partial regularity for solutions of quasilinear parabolic systems with nonsmooth in time principal matrix

Nonlinear Analysis: Theory, Methods & Applications, 2014

Partial regularity for solutions of quasilinear parabolic systems with nonsmooth in time principa... more Partial regularity for solutions of quasilinear parabolic systems with nonsmooth in time principal matrix is proved in the paper. Only boundedness of this matrix is assumed in time variable. To prove the result, we apply the method of modified A-caloric approximation assuming that the matrix A is not the constant one but depends on the time variable t.

Research paper thumbnail of On the Hölder continuity of gradient of solutions to a class of elliptic systems

Functiones et Approximatio Commentarii Mathematici, 2009

The interior C 1,γ-regularity for weak solutions with BMO-gradient of nonlinear nonautonomous sec... more The interior C 1,γ-regularity for weak solutions with BMO-gradient of nonlinear nonautonomous second order systems satisfying Legendre-Hadamard ellipticity condition is investigated.

Research paper thumbnail of Interior C 1, γ -Regularity for Weak Solutions of Nonlinear Second Order Parabolic Systems

Communications in Partial Differential Equations, 2006

ABSTRACT The interior C -regularity for the first gradient with respect to the space variables of... more ABSTRACT The interior C -regularity for the first gradient with respect to the space variables of a weak solution to a class of nonlinear second order parabolic systems is proven under the assumption that oscillations of coefficients are controlled by the ellipticity constant.

Research paper thumbnail of Morrey space regularity for weak solutions of Stokes systems with VMO coefficients

Annali di Matematica Pura ed Applicata

We prove that for weak solutions (u, p) of Stokes system with symmetric elliptic coefficients mat... more We prove that for weak solutions (u, p) of Stokes system with symmetric elliptic coefficients matrix A whose entries are bounded and VMO functions and with right-hand side f in Morrey space L 2,μ their symmetric gradients Eu and p belong to the same Morrey space L 2,μ .

Research paper thumbnail of Remarks on C1,γ-Regularity of Weak Solutions to Elliptic Systems with BMO Gradients

Zeitschrift für Analysis und ihre Anwendungen, 2009

Research paper thumbnail of Function Spaces

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