Universal approximation of symmetrizations by polarizations

DOI10.1090/S0002-9939-05-08325-5zbMath1093.26012OpenAlexW2137644393MaRDI QIDQ5695757

Jean Van Schaftingen

Publication date: 6 October 2005

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-05-08325-5

zbMATH Keywords

symmetrization

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Methods involving semicontinuity and convergence; relaxation (49J45) Inequalities involving derivatives and differential and integral operators (26D10) Other special methods applied to PDEs (35A25)

Related Items (17)

Symmetrization inequalities and Sobolev embeddings ⋮ Explicit approximation of the symmetric rearrangement by polarizations ⋮ Convergence of symmetrization processes ⋮ On the symmetry and monotonicity of Morrey extremals ⋮ Steiner symmetrization using a finite set of directions ⋮ Oscillatory phenomena for higher-order fractional Laplacians ⋮ Results on the existence of the Yamabe minimizer of \(M^m \times \mathbb R^n\) ⋮ Rearrangements in metric spaces and in the Heisenberg group ⋮ Equivalence between Pólya-Szegő and relative capacity inequalities under rearrangement ⋮ RADIAL SYMMETRY OF MINIMAX CRITICAL POINTS FOR NONSMOOTH FUNCTIONALS ⋮ Extremal rearrangement problems involving Poisson's equation with Robin boundary conditions ⋮ Rearrangement and polarization ⋮ An unstable two-phase membrane problem and maximum flux exchange flow ⋮ A countable set of directions is sufficient for Steiner symmetrization ⋮ Anisotropic symmetrization ⋮ Symmetrization and harmonic measure ⋮ On the symmetry of minimizers in constrained quasi-linear problems

Cites Work

• Rearrangements of functions
• Partial symmetry and asymptotic behavior for some elliptic variational problems
• A general rearrangement inequality for multiple integrals
• Uniqueness and minimality of solutions of a Ginzburg-Landau equation
• An approach to symmetrization via polarization
• Isoperimetric Inequalities in Mathematical Physics. (AM-27)
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