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

Davide Guidetti

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

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

Dian K. Palagachev, Maria A. Ragusa, Lubomira G. Softova (2003)

Bollettino dell'Unione Matematica Italiana

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Let $Q_{T}$ be a cylinder in $R^{n + 1}$ and $x = (x^{'}, t) \in R^{n} \times R$ . It is studied the Cauchy-Dirichlet problem for the uniformly parabolic operator $\{\begin{matrix} u_{t} - \overset{n}{\sum_{i, j = 1}} a^{i j} (x) D_{i j} u = f (x) & q.o. in Q_{T}, \\ u (x) = 0 & su \partial Q_{T}, \end{matrix}$ in the Morrey spaces $W_{p, λ}^{2, 1} (Q_{T})$ , $p \in (1, \infty)$ , $λ \in (0, n + 2)$ , supposing the coefficients to belong to the class of functions with vanishing mean oscillation. There are obtained a priori estimates in Morrey spaces and Hölder regularity for the solution and its spatial derivatives.

On the initial-boundary value problems for a degenerate parabolic equation

Jan Goncerzewicz (2008)

Banach Center Publications

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For an equation of the type of porous media equation the Cauchy-Dirichlet and Cauchy-Neumann problems are considered. The existence and uniqueness results in the case of $L^{\infty}$ initial and boundary data are given.

Quasilinear parabolic equations

D. E. Edmunds, L. A. Peletier (1971)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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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.

Optimal regularity for mixed parabolic problems in spaces of functions which are Hölder continuous with respect to space variables

Davide Guidetti (1998)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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

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

On the initial-boundary value problems for a degenerate parabolic equation

Quasilinear parabolic equations

The L p solvability of the Dirichlet problems for parabolic equations

Optimal regularity for mixed parabolic problems in spaces of functions which are Hölder continuous with respect to space variables

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