A symmetry problem in potential theory

1971/01/01 by James Serrin · 82 citations
Physics and Astronomy · #Quantum chaos and dynamical systems

paper · doi:10.1007/bf00250468

Cited by

• Asymptotic behavior of solutions to the σ k -Yamabe equation near isolated singularities
• Liouville-type theorems and harnack-type inequalities for semilinear elliptic equations
• Classification of solutions for an integral equation
• Ball and Spherical-Shell Rigidity from Overdetermined Translating Solitons
• Hadamard variational formulas for p-torsion and p-eigenvalue with applications
• Serrin problems with vertical boundary behavior
• Serrin's Problem under Dirichlet Perturbations: Geometric Compactness and Sharp Planar Stability
• Critical points of the second Neumann eigenfunctions on the quadrangles with symmetry
• Rigidity for capillary liquid drops of nearly circular section with constant vorticity
• Piecewise smooth stationary Euler flows with support in a neighborhood of a helix
• Asymptotic estimates for the plasma problem
• Serrin’s result for hyperbolic space and sphere
• Convex combinations of low eigenvalues, Fraenkel asymmetries and\n attainable sets
• Uniqueness theorems through the method of moving spheres
• Stationary soap films with vertical potentials
• Symmetry in stationary and uniformly-rotating solutions of active scalar equations
• Problems related to isoparametric theory
• Asymptotic analysis of solutions related to the game-theoretic p-laplacian
• Mixed local-nonlocal operators: maximum principles, eigenvalue problems and their applications
• Large-Amplitude Steady Solitary Water Waves with General Vorticity
• An overdetermined problem related to the p-Laplacian on Riemannian manifolds
• Bifurcating domains for an overdetermined eigenvalue problem in cylinders
• Unbounded Branches of Non-Radial Solutions to Semilinear Elliptic Systems on a Unit Ball in \mathbb R³ and Their Patterns
• Exact solution structures on some nonlocal overdetermined problems
• Payne-Philippin's overdetermined problems on compact surfaces
• On the Schiffer and Berenstein conjectures for centrally symmetric convex domains in the plane
• Non-isoparametric Serrin domains of \mathbbS³ with connected toric boundary
• Dynamics of Ideal Fluid Flows
• K-surfaces with free boundaries
• Qualitative properties of positive solutions to nonlocal critical\n problems involving the Hardy-Leray potential
• Radial symmetry of positive solutions to quasilinear Hardy-Sobolev doubly critical systems
• A characterization of the delaunay surfaces
• Second variation of domain functionals and applications to problems with Robin boundary conditions
• Monotonicity and nonexistence results for some fractional elliptic\n problems in the half space
• Monotonicity in half-spaces of positive solutions to -Δ_p u=f(u) in the case p>2
• Symmetry and linear stability in Serrin's overdetermined problem via the\n stability of the parallel surface problem
• Symmetries in an overdetermined problem for the Green's function
• Remark on some conformally invariant integral equations: the method of moving spheres
• Alexandrov, Serrin, Weinberger, Reilly: simmetry and stability by integral identities
• Optimal concavity of the torsion function
• Global rigidity of two-dimensional bubbles
• Monotonicity and Liouville-type theorems for semilinear elliptic problems in the half space
• On the Serrin's problem with Robin boundary conditions
• From fractional Lane-Emden-Serrin equation -- existence, multiplicity and local behaviors via classical ODE -- to fractional Yamabe metrics with singularity of "maximal" dimension
• Monotonicity properties of the Robin torsion function in a class of symmetric planar domains
• Maximum principles and monotonicity of solutions for fractional p-equations in unbounded domains
• New Homogeneous Solutions for the One-Phase Free Boundary Problem
• On the Serrin problem for ring-shaped domains
• Serrin's overdetermined theorem within Lipschitz domains
• A nonlinear Liouville theorem for fractional equations in the Heisenberg group
• Overdetermined fractional Serrin problem
• On Serrin’s overdetermined problem in space forms
• Non-symmetric solutions to an overdetermined problem for the Helmholtz equation in the plane
• On p-Willmore Disks with Boundary Energies
• Symmetry of large solutions for semilinear elliptic equations in a ball
• The Maximum Principles and Symmetry results for Viscosity Solutions of Fully Nonlinear Equations
• Symmetry and uniqueness of minimizers of Hartree type equations with\n external Coulomb potential
• Compact λ-translating solitons with boundary
• Monotonicity in half-spaces for singular quasilinear elliptic problems involving the gradient
• A unified approach to symmetry for semilinear equations associated to the Laplacian in ℝ^N
• On the H "opf Boundary Lemma for quasilinear problems involving\n singular nonlinearities and applications
• Symmetry and monotonicity of singular solutions for the Hartree equation
• Wulff shape characterizations in overdetermined anisotropic elliptic\n problems
• Symmetry via antisymmetric maximum principles in nonlocal problems of variable order
• The fully nonlinear Loewner-Nirenberg problem: Liouville theorems and counterexamples to local boundary estimates
• A partially overdetermined problem in a half ball
• On Payne-Schaefer's Conjecture about an Overdetermined Boundary Problem of Sixth Order
• On the behaviour of clamped plates under large compression
• Existence and Symmetry results for some overdetermined free boundary problems
• New trends in free boundary problems
• Classification of the solutions to an overdetermined problem in the plane
• How to place an obstacle having a dihedral symmetry centered at a given point inside a disk so as to optimize the fundamental Dirichlet eigenvalue
• Some characterizations of parallel hyperplanes in multi-layered heat conductors
• Fractional Dirichlet problems with an overdetermined nonlocal Neumann condition
• Serrin-type problem in divergence form on Riemannian manifolds
• Linear stability estimates for Serrin's problem via a modified implicit function theorem
• A rigidity result for overdetermined elliptic problems in the plane
• The moving plane method for singular semilinear elliptic problems
• The classical overdetermined Serrin problem
• Symmetries in some extremal problems between two parallel hyperplanes
• Pohozaev identity for the anisotropic p-Laplacian and estimates of torsion function
• Symmetry results for nonvariational quasi-linear elliptic systems