Elliptic equations on manifolds and isoperimetric inequalities

DOI10.1017/S0308210500024392zbMath0709.58037MaRDI QIDQ3492454

Andrea Cianchi

Publication date: 1990

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

a priori estimatesRiemannian manifoldsNeumann boundary conditionsisoperimetric inequalitieselliptic equationseigenvalue estimates

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Global differential geometry of Hermitian and Kählerian manifolds (53C55) A priori estimates in context of PDEs (35B45) Boundary values of solutions to elliptic equations and elliptic systems (35J67) Boundary value problems on manifolds (58J32)

Related Items (12)

Optimal summability of solutions to nonlinear elliptic problems ⋮ Quasilinear elliptic problems with general growth and merely integrable, or measure, data ⋮ Neumann comparison theorems in elliptic PDEs ⋮ Optimal Sobolev embeddings for the Ornstein-Uhlenbeck operator ⋮ Gradient regularity via rearrangements for \(p\)-Laplacian type elliptic boundary value problems ⋮ Sharp exponential inequalities for the Ornstein-Uhlenbeck operator ⋮ Neumann problems and isocapacitary inequalities ⋮ Pointwise symmetrization inequalities for Sobolev functions and applications ⋮ Well-posed elliptic Neumann problems involving irregular data and domains ⋮ Second-order two-sided estimates in nonlinear elliptic problems ⋮ Symmetrization inequalities for difference equations on graphs ⋮ Global gradient estimates in elliptic problems under minimal data and domain regularity

Cites Work

• Spectral geometry: direct and inverse problems. With an appendix by G. Besson
• Nonlinear elliptic equations, rearrangements of functions and Orlicz spaces
• Beweis der isoperimetrischen Eigenschaft der Kugel im hyperbolischen und sphärischen Raum jeder Dimensionszahl
• Inégalités isopérimétriques et applications
• Einfacher Beweis der isoperimetrischen Eigenschaft der Kugel im euklidischen Raum von n Dimensionen. Dem Andenken an Charlotte Freifrau von Romberg gewidmet

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