Diego Pallara - Academia.edu (original) (raw)

Papers by Diego Pallara

Journal De Mathematiques Pures Et Appliquees, 2007

Let Ω be a smooth open bounded set in RN, let ϱ be the (smoothed in the interior) distance functi... more Let Ω be a smooth open bounded set in RN, let ϱ be the (smoothed in the interior) distance function from ∂Ω, let (aij) be a uniformly elliptic matrix with continuous entries in Ω and A the associated second order elliptic operator. Under suitable conditions, we prove that the operator L=−ϱA+B, with B a first order operator with continuous coefficients,

We give estimates on the bottom of the essential spectrum of Schrodinger operators +V in L2(RN ).

Journal of Mathematical Analysis and Applications, 2008

We consider a strictly elliptic operatorAu=∑ijDi(aijDju)−b⋅∇u+div(c⋅u)−Vu, where 0⩽V∈Lloc∞, aij∈C... more We consider a strictly elliptic operatorAu=∑ijDi(aijDju)−b⋅∇u+div(c⋅u)−Vu, where 0⩽V∈Lloc∞, aij∈Cb1(RN), b,c∈C1(RN,RN). If divb⩽βV, divc⩽βV, 0β1, then a natural realization of A generates a positive C0-semigroup T in L2(RN). The semigroup satisfies pseudo-Gaussian estimates if|b|⩽k1Vα+k2,|c|⩽k1Vα+k2, where 12⩽α1. If α=12, then Gaussian estimates are valid. The constant α=12 is optimal with respect to this property.

We study global regularity properties of transitions kernels associated with second-order differe... more We study global regularity properties of transitions kernels associated with second-order differential operators in R N with unbounded drift and potential terms. Under suitable conditions, we prove Sobolev regularity of transition kernels and pointwise upper bounds. As an application, we obtain sufficient conditions implying the differentiability of the associated semigroup on the space of bounded and continuous functions on R

We give sufficient conditions for the discreteness of the spectrum of differentialoperators of th... more We give sufficient conditions for the discreteness of the spectrum of differentialoperators of the form Au = \Gamma\Deltau +hrF;rui in L2 (Rn) where d(x) = e\GammaF (x)dx andfor Schrodinger operators in L2(Rn). Our conditions are also necessary in the case ofpolynomial coefficients.Mathematics subject classification (1991): 35P05, 35J10, 35J701 IntroductionIn this paper we study the discreteness of the spectrum of two

... Luigi Ambrosio Dipartimento di Matematica \F. Casorati&quot;, Via Abbiategrasso 205 2... more ... Luigi Ambrosio Dipartimento di Matematica \F. Casorati&quot;, Via Abbiategrasso 205 27100 Pavia, Italy Nicola Fusco Dipartimento di Matematica \U. Dini&quot;, Viale Morgagni 67/A 50134 Firenze, Italy Diego Pallara Dip. di Matematica Universit a di Lecce CP 193, 73100 Lecce, Italy ...

Mathematische Nachrichten, 2000

Journal of Geometric Analysis, 1998

Theory of Probability and Its Applications, 2010

We prove global Sobolev regularity and pointwise upper bounds for transition densities associated... more We prove global Sobolev regularity and pointwise upper bounds for transition densities associated with second order dierential operators in RN with unbounded drift. As an application, we obtain sucient conditions implying the dierentiability

$Research paper thumbnail of THE SECTOR OF ANALYTICITY OF THE ORNSTEIN–UHLENBECK SEMIGROUP ON <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>L</mi><mi>p</mi></msup></mrow><annotation encoding="application/x-tex">L^{p}</annotation></semantics></math>Lp SPACES WITH RESPECT TO INVARIANT MEASURE$

Journal of The London Mathematical Society-second Series, 2005

The sector of analyticity of the Ornstein-Uhlenbeck semigroup is computed on the space Lp µ := Lp... more The sector of analyticity of the Ornstein-Uhlenbeck semigroup is computed on the space Lp µ := Lp (RN ; µ) with respect to its invariant measure µ .I fA =∆ +Bx ·∇ denotes the generator of the Ornstein-Uhlenbeck semigroup, then the angle θ2 of the sector of analyticity in L2 µ is π/2 minus the spectral angle of BQ∞, Q∞

Semigroup Forum, 2002

We present in a unified way, and in a purely analytic setting, some aspects of the theory of semi... more We present in a unified way, and in a purely analytic setting, some aspects of the theory of semigroups generated in the space of bounded continuous functions by second order elliptic operators with unbounded coefficients in R N , and the associated resolvent equation. Many examples are also presented. : 35K65, 47D07, 60J35.

Journal of Functional Analysis, 2002

Let A=∑i,j=1NqijDij+∑i,j=1NbijxjDi be a possibly degenerate Ornstein–Uhlenbeck operator in RN and... more Let A=∑i,j=1NqijDij+∑i,j=1NbijxjDi be a possibly degenerate Ornstein–Uhlenbeck operator in RN and assume that the associated Markov semigroup has an invariant measure μ. We compute the spectrum of A in Lμp for 1⩽p<∞.

We study the generation of an analytic semigroup in Lp(Rd) and the de- termination of the domain ... more We study the generation of an analytic semigroup in Lp(Rd) and the de- termination of the domain for a class of second order elliptic operators with unbounded coecien ts in Rd. We also establish the maximal regularity of type Lq{Lp for the corre- sponding inhomogeneous parabolic equation. In contrast to the previous literature the coecien ts of the second derivatives

We prove short time estimates for the heat kernel of Schrödinger operators with unbounded potenti... more We prove short time estimates for the heat kernel of Schrödinger operators with unbounded potential in R N . Mathematics Subject Classification (2000): 35K65, 35B65, 47D07, 60J35.

We study global regularity properties of invariant measures associated with second order differen... more We study global regularity properties of invariant measures associated with second order differential operators in R N . Under suitable conditions, we prove global boundedness of the density, Sobolev regularity, a Harnack inequality and pointwise upper and lower bounds.

Communications on Pure and Applied Analysis, 2014