The ${L}^p$ Neumann problem for the heat equation in non-cylindrical domains

Steve Hofmann; John L. Lewis

Displaying similar documents to “The $L^{p}$ Neumann problem for the heat equation in non-cylindrical domains”

The Dirichlet problem for the biharmonic equation in a Lipschitz domain

Björn E. J. Dahlberg, C. E. Kenig, G. C. Verchota (1986)

Annales de l'institut Fourier

Similarity:

In this paper we study and give optimal estimates for the Dirichlet problem for the biharmonic operator $Δ^{2}$ , on an arbitrary bounded Lipschitz domain $D$ in $R^{n}$ . We establish existence and uniqueness results when the boundary values have first derivatives in $L^{2} (\partial D)$ , and the normal derivative is in $L^{2} (\partial D)$ . The resulting solution $u$ takes the boundary values in the sense of non-tangential convergence, and the non-tangential maximal function of $\nabla u$ is shown to be in $L^{2} (\partial D)$ .

The $\bar{\partial}$ -Neumann operator on Lipschitz $q$ -pseudoconvex domains

Sayed Saber (2011)

Czechoslovak Mathematical Journal

Similarity:

On a bounded $q$ -pseudoconvex domain $Ω$ in $ℂ^{n}$ with a Lipschitz boundary, we prove that the $\bar{\partial}$ -Neumann operator $N$ satisfies a subelliptic $(1 / 2)$ -estimate on $Ω$ and $N$ can be extended as a bounded operator from Sobolev $(- 1 / 2)$ -spaces to Sobolev $(1 / 2)$ -spaces.

$B^{q}$ for parabolic measures

Caroline Sweezy (1998)

Studia Mathematica

Similarity:

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...

Boundary value problems of linear elastostatics and hydrostatics on Lipschitz domains

Carlos E. Kenig (1983-1984)

Séminaire Équations aux dérivées partielles (Polytechnique)

Similarity:

An endpoint Littlewood-Paley inequality for BVP associated with the Laplacian on Lipschitz domains.

Pascal Auscher, Philippe Tchamitchian (1999)

Publicacions Matemàtiques

Similarity:

We prove a commutator inequality of Littlewood-Paley type between partial derivatives and functions of the Laplacian on a Lipschitz domain which gives interior energy estimates for some BVP. It can be seen as an endpoint inequality for a family of energy estimates.

Gradient estimates in parabolic problems with unbounded coefficients

M. Bertoldi, S. Fornaro (2004)

Studia Mathematica

Similarity:

We study, with purely analytic tools, existence, uniqueness and gradient estimates of the solutions to the Neumann problems associated with a second order elliptic operator with unbounded coefficients in spaces of continuous functions in an unbounded open set Ω in $ℝ^{N}$ .

Some pinching deformations of the Fatou function

Patricia Domínguez, Guillermo Sienra (2015)

Fundamenta Mathematicae

Similarity:

We are interested in deformations of Baker domains by a pinching process in curves. In this paper we deform the Fatou function $F (z) = z + 1 + e^{- z}$ , depending on the curves selected, to any map of the form $F_{p / q} (z) = z + e^{- z} + 2 π i p / q$ , p/q a rational number. This process deforms a function with a doubly parabolic Baker domain into a function with an infinite number of doubly parabolic periodic Baker domains if p = 0, otherwise to a function with wandering domains. Finally, we show that certain attracting domains can be deformed...

Boundary value problems in Lipschitz cylinders for three-dimensional parabolic systems.

Russell M. Brown, Zhongwei Shen (1992)

Revista Matemática Iberoamericana

Similarity:

We consider initial-boundary value problems for a parabolic system in a Lipschitz cylinder. When the space dimension is three, we obtain estimates for the solutions when the lateral data taken from the best possible range of L-spaces.

Boundary estimates for certain degenerate and singular parabolic equations

Benny Avelin, Ugo Gianazza, Sandro Salsa (2016)

Journal of the European Mathematical Society

Similarity:

We study the boundary behavior of non-negative solutions to a class of degenerate/singular parabolic equations, whose prototype is the parabolic $p$ -Laplacian equation. Assuming that such solutions continuously vanish on some distinguished part of the lateral part $S_{T}$ of a Lipschitz cylinder, we prove Carleson-type estimates, and deduce some consequences under additional assumptions on the equation or the domain. We then prove analogous estimates for non-negative solutions to a class of...

Lipschitz spaces of holomorphic and pluriharmonic functions on bounded symmetric domains in $C^{N}$ (N>1)

Josephine Mitchell (1981)

Annales Polonici Mathematici

Similarity:

Displaying similar documents to “The L p Neumann problem for the heat equation in non-cylindrical domains”

Displaying similar documents to “The $L^{p}$ Neumann problem for the heat equation in non-cylindrical domains”