Sobolev Inequalities in Familiar and Unfamiliar Settings

DOI10.1007/978-0-387-85648-3_11zbMath1165.26011OpenAlexW72239224MaRDI QIDQ3613587

Laurent Saloff-Coste

Publication date: 12 March 2009

Published in: Sobolev Spaces In Mathematics I (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-0-387-85648-3_11

zbMATH Keywords

Moser's iterationDirichlet spaceflat Sobolev inequalitiesSobolev inequalities on graphs

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items

On spectral estimates for Schrödinger-type operators: the case of small local dimension, Nonlocal quadratic forms with visibility constraint, On-diagonal asymptotics for heat kernels of a class of inhomogeneous partial differential operators, Smooth Fourier multipliers in group algebras via Sobolev dimension, The sharp Sobolev inequality on metric measure spaces with lower Ricci curvature bounds, Equivalence of optimal \(L^1\)-inequalities on Riemannian manifolds, The CLR inequality for dominated semigroups, Non ultracontractive heat kernel bounds by Lyapunov conditions, A new approach to pointwise heat kernel upper bounds on doubling metric measure spaces, Spectral theory of infinite quantum graphs, Poincaré inequality: from remote balls to all balls, A note on Sobolev type inequalities on graphs with polynomial volume growth, Intrinsic metric and one-dimensional diffusions, SPACE OF RICCI FLOWS (II)—PART A: MODULI OF SINGULAR CALABI–YAU SPACES

Cites Work

• Characterization of sub‐Gaussian heat kernel estimates on strongly recurrent graphs
• Riemannian geometry.
• On the relation between elliptic and parabolic Harnack inequalities
• Manifolds and graphs with slow heat kernel decay
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Schrödinger equation and the eigenvalue problem
• Rough isometries, and combinatorial approximations of geometries of non- compact Riemannian manifolds
• Gromov's theorem on groups of polynomial growth and elementary logic
• Small time heat kernel behavior on Riemannian complexes
• Ultracontractivity and embedding into \(L^\infty\)
• Heat kernel on manifolds with ends
• Isoperimetric inequalities and Markov chains
• Rough isometries and the parabolicity of Riemannian manifolds
• Hardy-Littlewood theory for semigroups
• On the parabolic kernel of the Schrödinger operator
• Upper bounds for symmetric Markov transition functions
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
• Isoperimetricity for groups and manifolds
• Harmonic functions on manifolds
• \(L^2\)-cohomology and Sobolev inequalities
• Heat kernel upper bounds on a complete non-compact manifold
• Dirichlet forms and symmetric Markov processes
• Existence of positive harmonic functions on groups and on covering manifolds
• Harmonic sections of polynomial growth
• The Rozenblum-Lieb-Cwikel inequality for Markov generators
• Weyl type bounds for harmonic functions
• Heat kernel on connected sums of Riemannian manifolds
• Lectures on analysis on metric spaces
• Elliptic partial differential equations of second order
• Riesz transform, Gaussian bounds and the method of wave equation
• Stability results for Harnack inequalities.
• Sobolev inequalities and Myers's diameter theorem for an abstract Markov generator
• Ultracontractivity and Nash type inequalities
• Sub-Gaussian estimates of heat kernels on infinite graphs
• Plancherel-type estimates and sharp spectral multipliers
• Harnack inequalities and sub-Gaussian estimates for random walks
• Sobolev and isoperimetric inequalities for Dirichlet forms on homogeneous spaces
• Sobolev inequalities on homogeneous spaces
• Parabolic Harnack inequality for divergence form second order differential operators
• Isometric Riemannian manifolds at infinity
• Analysis on local Dirichlet spaces. II: Upper Gaussian estimates for the fundamental solutions of parabolic equations
• A Saint-Venant type principle for Dirichlet forms on discontinuous media
• Analysis on local Dirichlet spaces. III: The parabolic Harnack inequality
• An exact sequence in \(L^2\)-cohomology
• Local behavior of solutions of quasi-linear equations
• The art of random walks.
• The discrete integral maximum principle and its applications
• Local behavior of solutions of quasilinear parabolic equations
• Continuity of Solutions of Parabolic and Elliptic Equations
• Nash type inequalities for fractional powers of non-negative self-adjoint operators
• Nonsmooth calculus
• A new proof of Gromov’s theorem on groups of polynomial growth
• Liouville theorems and spectral edge behavior on abelian coverings of compact manifolds
• Two-sided estimates of fundamental solutions of second-order parabolic equations, and some applications
• On Harnack's theorem for elliptic differential equations
• On the Upper Estimate of the Heat Kernel of a Complete Riemannian Manifold
• A note on the isoperimetric constant
• Harnack's Inequality for Degenerate Parabolic Equations
• Bounds For The Fundamental Solution Of Degenerate Parabolic Equations
• Croissance polynomiale et périodes des fonctions harmoniques
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
• Sobolev Inequalities and Harmonic Functions of Polynomial Growth
• Weighted sobolev-poincaré inequalities for grushin type operators
• Analysis on local Dirichlet spaces. I. Recurrence, conservativeness and Lp-Liouville properties.
• L^2 harmonics forms on non compact manifolds
• Sobolev met Poincaré
• Mean value and Harnack inequalities for degenerate parabolic equations
• Sobolev inequalities in disguise
• Random Walks on Infinite Graphs and Groups
• A harnack inequality for parabolic differential equations
• Correetion to “A Harnack Inequality for Parabolic Differential Equations”
• On a pointwise estimate for parabolic differential equations