Contractive properties for the heat equation in Sobolev spaces

DOI10.1016/0022-1236(85)90067-9zbMath0577.46037OpenAlexW2083878089MaRDI QIDQ1066052

Hans Engler

Publication date: 1985

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(85)90067-9

zbMATH Keywords

mean curvaturezero Neumann boundary conditionsequivalent norms to the \(W^{1,p}\)-normheat semigroup with zero Dirichlet

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Heat equation (35K05) Groups and semigroups of linear operators (47D03)

Related Items (3)

Gradient estimates for solutions of parabolic equations and systems ⋮ Weak solutions of a class of quasilinear hyperbolic integro-differential equations describing viscoelastic materials ⋮ On the \(L^p-L^q\) estimates of the gradient of solutions to the Stokes problem

Cites Work

• Continuity of the gradient for weak solutions of a degenerate parabolic equation
• Maximum principles and their applications
• Gradient estimates for degenerate diffusion equations. I
• Une inégalité pour les opérateurs elliptiques du second ordre
• Uniqueness of the solutions of ut−Δϕ(u) = 0 with initial datum a measure
• The problem of dirichlet for quasilinear elliptic differential equations with many independent variables
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