Hölder continuity of parabolic quasi-minimizers on metric measure spaces

DOI10.1016/j.jde.2022.09.019OpenAlexW4296638881MaRDI QIDQ2109354

Andreas Herán

Publication date: 21 December 2022

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2022.09.019

zbMATH Keywords

Hölder continuitymetric measure spacesparabolic quasi-minimizers

Mathematics Subject Classification ID

Regularity of solutions in optimal control (49N60) Analysis on metric spaces (30L99)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Higher integrability for vector-valued parabolic quasi-minimizers on metric measure spaces
• Hölder regularity for parabolic De Giorgi classes in metric measure spaces
• Nonlinear potential theory on metric spaces
• Degenerate parabolic equations
• Quasi-minima
• Poincaré inequalities, uniform domains and extension properties for Newton-Sobolev functions in metric spaces
• Parabolic Q-minima and minimal solutions to variational flow
• On the regularity of the minima of variational integrals
• Quasiconformal maps in metric spaces with controlled geometry
• Hölder continuity of local minimizers
• Differentiability of Lipschitz functions on metric measure spaces
• Harnack's inequality for parabolic De Giorgi classes in metric spaces
• Hölder continuity of parabolic quasi-minimizers
• Existence of parabolic minimizers on metric measure spaces
• Global higher integrability for non-quadratic parabolic quasi-minimizers on 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
• Linear and quasilinear elliptic equations
• Continuity of Solutions of Parabolic and Elliptic Equations
• Hölder estimates for nonlinear degenerate parabolic sytems.
• A new proof of the Hölder continuity of solutions to p-Laplace type parabolic equations
• A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations
• Sobolev met Poincaré
• Removable sets for the poincare inequality on metric spaces
• Sobolev Spaces on Metric Measure Spaces
• Parabolic comparison principle and quasiminimizers in metric measure spaces
• Regularity of quasi-minimizers on metric spaces