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

Xiang Tao

Displaying similar documents to “The $L^{p}$ solvability of the Dirichlet problems for parabolic equations”

Quasilinear parabolic equations

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

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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$B^{q}$ for parabolic measures

Caroline Sweezy (1998)

Studia Mathematica

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If Ω is a Lip(1,1/2) domain, μ a doubling measure on $\partial_{p} Ω, \partial / \partial t - L_{i}$ , i = 0,1, are two parabolic-type operators with coefficients bounded and measurable, 2 ≤ q < ∞, then the associated measures $ω_{0}$ , $ω_{1}$ have the property that $ω_{0} \in B^{q} (μ)$ implies $ω_{1}$ is absolutely continuous with respect to $ω_{0}$ whenever a certain Carleson-type condition holds on the difference function of the coefficients of $L_{1}$ and $L_{0}$ . Also $ω_{0} \in B^{q} (μ)$ implies $ω_{1} \in B^{q} (μ)$ whenever both measures are center-doubling measures. This is B. Dahlberg’s result for elliptic measures...

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.

Full regularity of bounded solutions to nondiagonal parabolic systems of two equations

Dmitry Portnyagin (2008)

Applicationes Mathematicae

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Hölder continuity and, basing on this, full regularity and global existence of weak solutions is studied for a general nondiagonal parabolic system of nonlinear differential equations with the matrix of coefficients satisfying special structure conditions and depending on the unknowns. A technique based on estimating a certain function of unknowns is employed to this end.

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.

Parabolic sublinear operators with rough kernel generated by parabolic calderön-zygmund operators and parabolic local campanato space estimates for their commutators on the parabolic generalized local morrey spaces

Ferit Gurbuz (2016)

Open Mathematics

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In this paper, the author introduces parabolic generalized local Morrey spaces and gets the boundedness of a large class of parabolic rough operators on them. The author also establishes the parabolic local Campanato space estimates for their commutators on parabolic generalized local Morrey spaces. As its special cases, the corresponding results of parabolic sublinear operators with rough kernel and their commutators can be deduced, respectively. At last, parabolic Marcinkiewicz operator...

Displaying similar documents to “The L p solvability of the Dirichlet problems for parabolic equations”

Quasilinear parabolic equations

B q for parabolic measures

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

Full regularity of bounded solutions to nondiagonal parabolic systems of two equations

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

Parabolic sublinear operators with rough kernel generated by parabolic calderön-zygmund operators and parabolic local campanato space estimates for their commutators on the parabolic generalized local morrey spaces

Displaying similar documents to “The $L^{p}$ solvability of the Dirichlet problems for parabolic equations”

$B^{q}$ for parabolic measures

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