Hölder regularity for parabolic De Giorgi classes in metric measure spaces

DOI10.1007/s00229-012-0598-2zbMath1275.35063arXiv1210.6792OpenAlexW2158484569MaRDI QIDQ361838

Mathias Masson, Juhana Siljander

Publication date: 19 August 2013

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.6792

zbMATH Keywords

doubling measureannular decay propertyweak \((1,p)\)-Poincaré inequality

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Degenerate parabolic equations (35K65) Quasilinear parabolic equations with (p)-Laplacian (35K92) Potential theory on fractals and metric spaces (31E05)

Related Items (19)

Global higher integrability for non-quadratic parabolic quasi-minimizers on metric measure spaces ⋮ Higher integrability for vector-valued parabolic quasi-minimizers on metric measure spaces ⋮ Variational solutions to the total variation flow on metric measure spaces ⋮ Time-smoothing for parabolic variational problems in metric measure spaces ⋮ Harnack inequality for parabolic quasi minimizers on metric spaces ⋮ Existence of parabolic minimizers to the total variation flow on metric measure spaces ⋮ On the Harnack inequality for parabolic minimizers in metric measure spaces ⋮ Harnack estimates for degenerate parabolic equations modeled on the subelliptic \(p\)-Laplacian ⋮ Stability for parabolic quasiminimizers ⋮ Local higher integrability for parabolic quasiminimizers in metric spaces ⋮ Harmonic functions on metric measure spaces ⋮ Local Calderón-Zygmund estimates for parabolic minimizers ⋮ Intrinsic geometry and De Giorgi classes for certain anisotropic problems ⋮ Hölder continuity of parabolic quasi-minimizers ⋮ Existence of parabolic minimizers on metric measure spaces ⋮ Existence of variational solutions to a Cauchy-Dirichlet problem with time-dependent boundary data on metric measure spaces ⋮ Parabolic comparison principle and quasiminimizers in metric measure spaces ⋮ Hölder continuity of parabolic quasi-minimizers on metric measure spaces ⋮ Global higher integrability for parabolic quasiminimizers in metric measure spaces

Cites Work

• Hölder continuity for Trudinger's equation in measure spaces
• Nonlinear potential theory on metric spaces
• Degenerate parabolic equations
• Degenerate parabolic equations and Harnack inequality
• A remark on a Harnack inequality for dengerate parabolic equations
• Parabolic Q-minima and minimal solutions to variational flow
• Quasiconformal maps in metric spaces with controlled geometry
• Differentiability of Lipschitz functions on metric measure spaces
• Lectures on analysis on metric spaces
• Definitions of Sobolev classes on metric spaces
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• The Poincaré inequality is an open ended condition
• The method of intrinsic scaling. A systematic approach to regularity for degenerate and singular PDEs
• Parabolic De Giorgi classes of order \(p\) and the Harnack inequality
• A Harnack inequality for degenerate parabolic equations
• The Dirichlet problem for p-harmonic functions on metric spaces
• Local Hoelder continuity for doubly nonlinear parabolic equations
• Regularity of quasi-minimizers on metric spaces
• Harmonic functions on metric spaces
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