Concepedia

Uniqueness in a Free Boundary Problem

John L. Lewis, Andrew Vogel

Communications in Partial Differential Equations · 2006 · 18 citations · 12 references

Concepts

Elliptic EquationRiemann-hilbert ProblemPositive SolutionsFree Boundary ProblemPotential TheoryOverdetermined Boundary ConditionsFunctional AnalysisP LaplacianNonlinear Functional Analysis

Abstract

We study overdetermined boundary conditions for positive solutions to the p Laplacian in a bounded domain D. We show these conditions imply uniqueness in certain free boundary problems.

References

12

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Symmetry Problem, Potential Theory, Symmetry (Physics) +2

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Emmanuele DiBenedetto · Nonlinear Analysis · 1983 · 1.1K citations

Degenerate Elliptic Equations, Elliptic Equation, Elliptic Function +4

Local behavior of solutions of quasi-linear equations

James Serrin · Acta Mathematica · 1964 · 1K citations · Full text

Capacitary functions in convex rings

John L. Lewis · Archive for Rational Mechanics and Analysis · 1977 · 200 citations

Commutative Algebra, Ring Theory, Convex Hull +2

Regularity of $p$-Harmonic Functions on the Plane

Tadeusz Iwaniec, Juan J. Manfredi · Revista Matemática Iberoamericana · 1989 · 137 citations · Full text

Spectral Theory, Engineering, Potential Theory +4