Existence of solutions of two-phase free boundary problems for fully nonlinear elliptic equations of second order

DOI10.1007/BF02921886zbMath1057.35099MaRDI QIDQ1429306

Pei-Yong Wang

Publication date: 18 May 2004

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

zbMATH Keywords

regularityHausdorff measureexistence of a weak solutionexistence of a classical solution

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Free boundary problems for PDEs (35R35) Hausdorff and packing measures (28A78)

Related Items (11)

Up to the boundary gradient estimates for viscosity solutions to nonlinear free boundary problems with unbounded measurable ingredients ⋮ Regularity of interfaces for a Pucci type segregation problem ⋮ On two phase free boundary problems governed by elliptic equations with distributed sources ⋮ On the uniqueness of a solution of a two-phase free boundary problem ⋮ Free boundary regularity for fully nonlinear non-homogeneous two-phase 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 ⋮ Hausdorff measure estimates and Lipschitz regularity in inhomogeneous nonlinear free boundary problems ⋮ 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

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• A Harnack inequality approach to the regularity of free boundaries. I: Lipschitz free boundaries are \(C^{1,\alpha}\)
• Barriers on cones for uniformly elliptic operators
• REGULARITY OF FREE BOUNDARIES OF TWO-PHASE PROBLEMS FOR FULLY NONLINEAR ELLIPTIC EQUATIONS OF SECOND ORDER. II. FLAT FREE BOUNDARIES ARE LIPSCHITZ
• A Harnack inequality approach to the regularity of free boundaries part II: Flat free boundaries are Lipschitz
• Variational problems with two phases and their free boundaries
• 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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