The structure of the singular set in the thin obstacle problem for degenerate parabolic equations

DOI10.1007/s00526-021-01938-2zbMath1469.35130arXiv1902.07457OpenAlexW3159508596WikidataQ115386755 ScholiaQ115386755MaRDI QIDQ829409

Agnid Banerjee, Nicola Garofalo, Donatella Danielli, Arshak Petrosyan

Publication date: 6 May 2021

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.07457

zbMATH Keywords

thin obstacle problem, fractional heat equation, monotonicity formula, singular set

Mathematics Subject Classification ID

Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators (35K85) Initial-boundary value problems for second-order parabolic equations (35K20) Degenerate parabolic equations (35K65) Free boundary problems for PDEs (35R35) Fractional partial differential equations (35R11)

Related Items (12)

\(H^{1+ \alpha}\) estimates for the fully nonlinear parabolic thin obstacle problem ⋮ The thin obstacle problem for some variable coefficient degenerate elliptic operators ⋮ Regularity for parabolic systems with critical growth in the gradient and applications ⋮ A note on monotonicity and Bochner formulas in Carnot groups ⋮ Borderline gradient continuity for fractional heat type operators ⋮ Regularity of almost minimizers for the parabolic thin obstacle problem ⋮ On the existence and Hölder regularity of solutions to some nonlinear Cauchy-Neumann problems ⋮ Quantitative uniqueness for fractional heat type operators ⋮ Higher regularity of the free boundary in the obstacle problem for the fractional heat operator ⋮ Two classical properties of the Bessel quotient 𝐼_{𝜈+1}/𝐼_{𝜈} and their implications in pde’s ⋮ An epiperimetric inequality approach to the parabolic Signorini problem ⋮ Space-like strong unique continuation for some fractional parabolic equations

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