Local Continuity of Weak Solutions to the Stefan Problem Involving the Singular $p$-Laplacian

DOI10.1137/21M1402443zbMath1487.35186arXiv2103.00412MaRDI QIDQ5073754

Naian Liao

Publication date: 3 May 2022

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.00412

zbMATH Keywords

Stefan problemparabolic \(p\)-Laplaciandoubly singular parabolic equationintrinsic scalinglocal continuity\(L^1\) Harnack inequality

Mathematics Subject Classification ID

PDEs with multivalued right-hand sides (35R70) Stefan problems, phase changes, etc. (80A22) Free boundary problems for PDEs (35R35) Weak solutions to PDEs (35D30) Quasilinear parabolic equations with (p)-Laplacian (35K92) Quasilinear parabolic equations (35K59)

Related Items (1)

Existence of variational solutions to doubly nonlinear nonlocal evolution equations via minimizing movements

Cites Work

• A quantitative modulus of continuity for the two-phase Stefan problem
• Degenerate parabolic equations
• On the continuity of solutions to doubly singular parabolic equations
• Continuity of the temperature in the two-phase Stefan problem
• Continuity of weak solutions to certain singular parabolic equations
• Continuous solutions for a degenerate free boundary problem
• On the singular equation \(\beta (u)_ t=\Delta u\)
• Harnack's Inequality for Degenerate and Singular Parabolic Equations
• On the Doubly Singular Equation γ(u)_t= Δ_pu
• Unnamed Item

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