Pointwise estimates for Laplace equation. Applications to the free boundary of the obstacle problem with Dini coefficients

DOI10.1007/s00041-009-9066-0zbMath1178.35142OpenAlexW1964062968MaRDI QIDQ731266

Régis Monneau

Publication date: 2 October 2009

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00041-009-9066-0

zbMATH Keywords

Liouville theoremLaplace equationfree boundaryobstacle problemDini regularitypointwise modulus of continuitypointwise modulus of mean oscillationpointwise regularity property

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45) Second-order elliptic equations (35J15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Free boundary problems for PDEs (35R35)

Related Items (14)

The structure of the singular set in the thin obstacle problem for degenerate parabolic equations ⋮ Some new monotonicity formulas and the singular set in the lower dimensional obstacle problem ⋮ The classical obstacle problem with coefficients in fractional Sobolev spaces ⋮ Optimal Regularity and the Free Boundaryin the Parabolic Signorini Problem ⋮ Unnamed Item ⋮ Regularity estimates for nonlocal Schrödinger equations ⋮ Atomic to continuum passage for nanotubes: a discrete Saint-Venant principle and error estimates ⋮ Pointwise regularity of the free boundary for the parabolic obstacle problem ⋮ New monotonicity formulas and the optimal regularity in the Signorini problem with variable coefficients ⋮ Regularity in parabolic Dini continuous systems ⋮ The thin obstacle problem: a survey ⋮ The classical obstacle problem with Hölder continuous coefficients ⋮ Equilibrium points of a singular cooperative system with free boundary ⋮ Pointwise estimates for degenerate Kolmogorov equations with \(L^p\)-source term

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