Some new symmetry results for elliptic problems on the sphere and in Euclidean space

DOI10.1007/BF02904257zbMath1008.35002MaRDI QIDQ1851400

Jyotshana V. Prajapat, Friedemann Brock

Publication date: 17 December 2002

Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)

zbMATH Keywords

maximum principlerearrangementstereographic projectionelliptic equationuniqueness of the solutionsymmetry of the solution

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear boundary value problems for linear elliptic equations (35J65) Maximum principles in context of PDEs (35B50) Nonlinear elliptic equations (35J60) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (9)

Characterization of stadium-like domains via boundary value problems for the infinity Laplacian ⋮ A symmetry property for fully nonlinear elliptic equations on the sphere ⋮ On the Dirichlet and Serrin problems for the inhomogeneous infinity Laplacian in convex domains: regularity and geometric results ⋮ Multiple Clustered Layer Solutions for Semilinear Elliptic Problems onSⁿ ⋮ Serrin-type theorems for triangles ⋮ Radial symmetry of positive solutions for semilinear elliptic equations in the unit ball via elliptic and hyperbolic geometry ⋮ Non-radial clustered spike solutions for semilinear elliptic problems on \(S^N\) ⋮ A symmetry problem in the calculus of variations ⋮ Some connections between symmetry results for semilinear PDE in real and hyperbolic spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Symmetry and related properties via the maximum principle
• Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results
• On maximum principles and existence of positive solutions for some cooperative elliptic systems
• Continuous rearrangement and symmetry of solutions of elliptic problems
• Symmetry or not?
• Serrin's result for hyperbolic space and sphere
• A strong maximum principle for some quasilinear elliptic equations
• A symmetry problem in potential theory
• Quasilinear elliptic equations involving critical Sobolev exponents
• Symmetry and Overdetermined Boundary Value Problems
• Some notes on the method of moving planes
• Symmetry properties of positive solutions of elliptic equations on symmetric domains
• Green’s function, harmonic transplantation, and best Sobolev constant in spaces of constant curvature
• Existence and uniqueness of positive radial solutions for a class of quasilinear elliptic equations
• A Symmetry Result Related to Some Overdetermined Boundary Value Problems
• Continuous Steiner‐Symmetrization
• Symmetry of positive solutions of a quasilinear elliptic equation via isoperimetric inequalities
• A symmetry result for the p-laplacian equation via the moving planes method
• An approach to symmetrization via polarization
• On the method of moving planes and the sliding method

This page was built for publication: Some new symmetry results for elliptic problems on the sphere and in Euclidean space