REGULARITY OF FREE BOUNDARIES OF TWO-PHASE PROBLEMS FOR FULLY NONLINEAR ELLIPTIC EQUATIONS OF SECOND ORDER. II. FLAT FREE BOUNDARIES ARE LIPSCHITZ
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Publication:3149938
DOI10.1081/PDE-120005846zbMath1125.35424OpenAlexW2015462759MaRDI QIDQ3149938
Publication date: 29 September 2002
Published in: Communications in Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1081/pde-120005846
Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60) Free boundary problems for PDEs (35R35)
Related Items (20)
Regularity of the free boundary in two-phase problems for linear elliptic operators ⋮ Up to the boundary gradient estimates for viscosity solutions to nonlinear free boundary problems with unbounded measurable ingredients ⋮ The classical obstacle problem with coefficients in fractional Sobolev spaces ⋮ Regularity of Lipschitz free boundaries for a \(p(x)\)-Laplacian problem with right hand side ⋮ Regularity of interfaces for a Pucci type segregation problem ⋮ Regularity of flat free boundaries in two-phase problems for the \(p\)-Laplace operator ⋮ Fully nonlinear singularly perturbed equations and asymptotic free boundaries ⋮ Existence of solutions of two-phase free boundary problems for fully nonlinear elliptic equations of second order ⋮ Bernstein-type techniques for 2D free boundary graphs ⋮ Regularity of flat free boundaries for a \(p(x)\)-Laplacian problem with right hand side ⋮ Two-phase free boundary problems: from existence to smoothness ⋮ On the uniqueness of a solution of a two-phase free boundary problem ⋮ Free boundary regularity for fully nonlinear non-homogeneous two-phase problems ⋮ Regularity of the Solutions for Parabolic Two-Phase Free Boundary Problems ⋮ Gradient estimates for viscosity solutions of singular fully nonlinear elliptic equations ⋮ Free boundary theory for non-homogeneous fully non-linear equations with unbounded ingredients and quadratic growth in the gradient ⋮ Monotonicity formulas for obstacle problems with Lipschitz coefficients ⋮ Existence of viscosity solutions to two-phase problems for fully nonlinear equations with distributed sources ⋮ The zero level set for a certain weak solution, with applications to the Bellman equations ⋮ Recent results on nonlinear elliptic free boundary problems
Cites Work
- A Harnack inequality approach to the regularity of free boundaries. I: Lipschitz free boundaries are \(C^{1,\alpha}\)
- A Harnack inequality approach to the regularity of free boundaries part II: Flat free boundaries are Lipschitz
- Regularity of free boundaries of two‐phase problems for fully nonlinear elliptic equations of second order I. Lipschitz free boundaries are C1,
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