A parabolic two-phase obstacle-like equation

DOI10.1016/j.aim.2009.01.011zbMath1168.35452OpenAlexW1982898812WikidataQ56967365 ScholiaQ56967365MaRDI QIDQ1018420

Henrik Shahgholian, Nina N. Ural'tseva, Georg Sebastian Weiss

Publication date: 19 May 2009

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2009.01.011

zbMATH Keywords

regularitybranch pointglobal solutionblow-upsingular pointfree boundaryobstacle problemmembrane

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Free boundary problems for PDEs (35R35) Second-order parabolic equations (35K10)

Related Items (6)

Uniform estimates near the initial state for solutions of the two-phase parabolic problem ⋮ Free boundaries in problems with hysteresis ⋮ A two-phase parabolic free boundary problem with coefficients below the Lipschitz threshold ⋮ Pointwise regularity of the free boundary for the parabolic obstacle problem ⋮ Spatially discrete reaction-diffusion equations with discontinuous hysteresis ⋮ Regularity issues for semilinear PDE-s (a narrative approach)

Cites Work

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• Global solutions of an obstacle-problem-like equation with two phases
• A parabolic almost monotonicity formula
• The two-phase membrane problem--an intersection-comparison approach to the regularity at branch points
• Self-Similar Blow-Up and Hausdorff Dimension Estimates for a Class of Parabolic Free Boundary Problems
• C^{1, 1} Regularity in semilinear elliptic problems
• Regularity of a free boundary in parabolic potential theory
• Lipschitz property of the free boundary in the parabolic obstacle problem
• The Two-Phase Membrane Problem--Regularity of the Free Boundaries in Higher Dimensions

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