Cauchy-Dirichlet problem in Morrey spaces for parabolic equations with discontinuous coefficients

Dian K. Palagachev; Maria A. Ragusa; Lubomira G. Softova

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The parabolic mixed Cauchy-Dirichlet problem in spaces of functions which are hölder continuous with respect to space variables

Davide Guidetti (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We give a new proof, based on analytic semigroup methods, of a maximal regularity result concerning the classical Cauchy-Dirichlet's boundary value problem for second order parabolic equations. More specifically, we find necessary and sufficient conditions on the data in order to have a strict solution $u$ which is bounded with values in $C^{2 + θ} (\bar{Ω})$ (0 < < 1), with $\partial_{t} u$ bounded with values in $C^{θ} (\bar{Ω})$ .

The $L^{p}$ solvability of the Dirichlet problems for parabolic equations

Xiang Tao (2000)

Studia Mathematica

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For two general second order parabolic equations in divergence form in Lip(1,1/2) cylinders, we give a criterion for the preservation of $L^{p}$ solvability of the Dirichlet problems.

Dirichlet problem for parabolic equations with continuous coefficients

Julio E. Bouillet (1976)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Observations on $W^{1, p}$ estimates for divergence elliptic equations with VMO coefficients

P. Auscher, M. Qafsaoui (2002)

Bollettino dell'Unione Matematica Italiana

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In this paper, we make some observations on the work of Di Fazio concerning $W^{1, p}$ estimates, $1 < p < \infty$ , for solutions of elliptic equations $div A \nabla u = div f$ , on a domain $Ω$ with Dirichlet data $0$ whenever $A \in V M O (Ω)$ and $f \in L^{p} (Ω)$ . We weaken the assumptions allowing real and complex non-symmetric operators and $C^{1}$ boundary. We also consider the corresponding inhomogeneous Neumann problem for which we prove the similar result. The main tool is an appropriate representation for the Green (and Neumann) function on the upper half space....

$L^{p}$ regularity for weak solutions of parabolic systems

Sergio Campanato (1980)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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The Calderón-Zygmund theorem and parabolic equations in $L P (ℝ, C^{2 + α})$ -spaces

Nicolai V. Krylov (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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A Banach-space version of the Calderón-Zygmund theorem is presented and applied to obtaining apriori estimates for solutions of second-order parabolic equations in $L_{p} (ℝ, C^{2 + α})$ -spaces.

Displaying similar documents to “Cauchy-Dirichlet problem in Morrey spaces for parabolic equations with discontinuous coefficients”

The parabolic mixed Cauchy-Dirichlet problem in spaces of functions which are hölder continuous with respect to space variables

The L p solvability of the Dirichlet problems for parabolic equations

Dirichlet problem for parabolic equations with continuous coefficients

Observations on W 1 , p estimates for divergence elliptic equations with VMO coefficients

L p regularity for weak solutions of parabolic systems

The Calderón-Zygmund theorem and parabolic equations in L P ( ℝ , C 2 + α ) -spaces

The $L^{p}$ solvability of the Dirichlet problems for parabolic equations

Observations on $W^{1, p}$ estimates for divergence elliptic equations with VMO coefficients

$L^{p}$ regularity for weak solutions of parabolic systems

The Calderón-Zygmund theorem and parabolic equations in $L P (ℝ, C^{2 + α})$ -spaces