Classical solutions to phase transition problems are smooth

DOI10.1080/03605309808821351zbMath0904.35014OpenAlexW2002266184MaRDI QIDQ4393220

Herbert Koch

Publication date: 8 June 1998

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605309808821351

zbMATH Keywords

Besov spacestwo-phase Stefan problemFourier multiplierdynamic boundary conditionNemytskij operatorsfrozen coefficients

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Free boundary problems for PDEs (35R35)

Related Items (8)

Existence of analytic solutions for the classical Stefan problem ⋮ Global stability of steady states in the classical Stefan problem for general boundary shapes ⋮ Local Well-Posedness and Global Stability of the Two-Phase Stefan Problem ⋮ Regularity of higher order in two-phase free boundary problems ⋮ On melting and freezing for the 2D radial Stefan problem ⋮ Two‐Phase Free Boundary Problems for Parabolic Operators: Smoothness of the Front ⋮ Recent results on nonlinear elliptic free boundary problems ⋮ Global Stability and Decay for the Classical Stefan Problem

Cites Work

• Unnamed Item
• Pseudo-differential operators of the exotic class \(L^ o_{1,1}\) in spaces of Besov and Triebel-Lizorkin type
• Classical solutions of the Stefan problem
• Parameter-elliptic and parabolic pseudodifferential boundary problems in global \(L_ p\) Sobolev spaces
• Regularity of the free boundary in parabolic phase-transition problems
• Caloric functions in Lipschitz domains and the regularity of solutions to phase transition problems
• Regular Elliptic Boundary Value Problems in Besov‐Triebel‐Lizorkin Spaces

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