Interior free boundary problems for the Laplace equation

DOI10.1007/BF00250477zbMath0397.76009OpenAlexW1994505887MaRDI QIDQ1253971

Andrew Acker

Publication date: 1981

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00250477

zbMATH Keywords

Bernoulli ConditionExistence ResultsHarmonic Measure

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Minimal surfaces and optimization (49Q05) Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing (76B10) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15)

Related Items (13)

Qualitative properties of the boundary derivative of the capacity potential for special classes of annular domains ⋮ On the Convexity and on the Successive Approximation of Solutions in a Free–Boundary Problem with Two Fluid Phases ⋮ Uniqueness and monotonicity of solutions for the interior bernoulli free boundary problem in the convex, n-dimensional case ⋮ On a Shape Derivative Formula in the Brunn--Minkowski Theory ⋮ How to approximate the solutions of certain free boundary problems for the Laplace equation by using the contraction principle ⋮ Bifurcation phenomena in a free boundary problem for a circulating flow with surface tension ⋮ Local existence and uniqueness theorems for a free boundary problem ⋮ On the multi-layer fluid problem: regularlty, uniqueness, convexity, and successive approximation of solutions ⋮ On a Bernoulli-type overdetermined free boundary problem ⋮ Free boundary optimization - a constructive iterative method ⋮ On the convexity of equilibrium plasma configurations ⋮ On the existence of convex classical solutions for multilayer free boundary problems with general nonlinear joining conditions ⋮ On the convexity of level lines of the fundamental mode in the clamped membrane problem, and the existence of convex solutions in a related free boundary problem

Cites Work

• Unnamed Item
• Free boundary optimization - a constructive iterative method
• Über ein Minimumproblem für Potentialströmungen mit freiem Rande
• Axially symmetric cavitational flow
• Concerning Daniljuk's Existence Theorem for Free Boundary-Value Problems with the Bernoulli Condition
• On a Free Boundary Problem, the Starlike Case
• A Free Boundary Optimization Problem
• Heat Flow Inequalities with Applications to Heat Flow Optimization Problems

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