A Saint-Venant type principle for Dirichlet forms on discontinuous media

DOI10.1007/BF01759352zbMath0851.31008OpenAlexW2091846918MaRDI QIDQ1913373

Umberto Mosco, Marco Biroli

Publication date: 14 May 1996

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01759352

zbMATH Keywords

Harnack inequalityGreen functionsenergy decaySaint-Venant principlemeasurable coefficientsDirichlet forms of diffusion typesecond order degenerate elliptic operators

Mathematics Subject Classification ID

Inhomogeneity in solid mechanics (74E05) Dirichlet forms (31C25) Degenerate elliptic equations (35J70) Connections of harmonic functions with differential equations in higher dimensions (31B35)

Related Items (only showing first 100 items - show all)

Sobolev Spaces in Extended Metric-Measure Spaces ⋮ A note on the topological stability theorem from RCD spaces to Riemannian manifolds ⋮ Harmonic functions with BMO traces and their limiting behaviors on metric measure spaces ⋮ Convergence of Riemannian manifolds and Laplace operators. I ⋮ Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces ⋮ A class of spatially inhomogeneous Dirichlet spaces on the \(p\)-adic number field. ⋮ Diffusion, optimal transport and Ricci curvature ⋮ Isoperimetric inequality from the poisson equation via curvature ⋮ Gauged Sobolev inequalities ⋮ Generalized Eigenfunctions and Spectral Theory for Strongly Local Dirichlet Forms ⋮ Parabolic Harnack inequality for divergence form second order differential operators ⋮ Dirichlet problem for Schrödinger equation with the boundary value in the BMO space ⋮ Asymptotic behaviour of relaxed Dirichlet problems involving a Dirichlet-Poincaré form ⋮ Liouville theorems for Fuchsian-type operators on the Heisenberg group ⋮ Generalized eigenfunctions and eigenvalues: a unifying framework for Shnol-type theorems ⋮ Hölder continuity and Harnack inequality for De Giorgi classes related to Hörmander vector fields ⋮ Sch'nol's theorem for strongly local forms ⋮ Unnamed Item ⋮ Harnack inequality for \(p\)-Laplacians associated to homogeneous \(p\)-Lagrangians ⋮ Indices of Dirichlet forms ⋮ Unnamed Item ⋮ Fractal snowflake domain diffusion with boundary and interior drifts ⋮ Self-improving properties of John-Nirenberg and Poincaré inequalities on spaces of homogeneous type ⋮ Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in \(\text{RCD}(K, \infty)\) metric measure spaces ⋮ Limits of variational problems for Dirichlet forms in varying domains ⋮ The heat semigroup and Brownian motion on strip complexes ⋮ Unnamed Item ⋮ Pointwise weak existence for diffusions associated with degenerate elliptic forms and 2-admissible weights ⋮ Angles between curves in metric measure spaces ⋮ Shnol-type theorem for the Agmon ground state ⋮ Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces ⋮ Degenerate elliptic operators in one dimension ⋮ Limits of relaxed Dirichlet problems involving a non symmetric Dirichlet form ⋮ Heat kernel estimates for the \({{\bar{\partial}}}\)-Neumann problem on \(G\)-manifolds ⋮ On the stochastic regularity of distorted Brownian motions ⋮ A note on the volume growth criterion for stochastic completeness of weighted graphs ⋮ Lecture notes on the DiPerna–Lions theory in abstract measure spaces ⋮ Harnack's inequality on homogeneous spaces ⋮ Gradient estimate for solutions to Poisson equations in metric measure spaces ⋮ Time-inhomogeneous stochastic processes on the \(p\)-adic number field ⋮ The Serre duality theorem for a non-compact weighted CR manifold ⋮ Harnack estimates for degenerate parabolic equations modeled on the subelliptic \(p\)-Laplacian ⋮ Isoperimetric inequality via Lipschitz regularity of Cheeger-harmonic functions ⋮ Stopping time convergence for processes associated with Dirichlet forms ⋮ Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces ⋮ Singular homogenization for Sierpinski pre-fractals ⋮ Cheeger-harmonic functions in metric measure spaces revisited ⋮ Vanishing and conservativeness of harmonic forms of a non-compact CR manifold ⋮ Brownian motion on some spaces with varying dimension ⋮ Widder's representation theorem for symmetric local Dirichlet spaces ⋮ Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds ⋮ Homogenization for conductive thin layers of pre-fractal type ⋮ Relaxation for Dirichlet problems involving a Dirichlet form ⋮ Harmonic maps from Riemannian polyhedra to geodesic spaces with curvature bounded from above ⋮ On Dirichlet forms and semi-Dirichlet forms. Remarks on the book ``Semi-Dirichlet forms and Markov processes by Yoichi Oshima ⋮ Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces ⋮ The penetration function and its application to microscale problems ⋮ Off-diagonal upper estimates for the heat kernel of the Dirichlet forms on metric spaces ⋮ Nonlinear subelliptic Schrödinger type problems ⋮ Essential Self-Adjointness of a Sublaplacian via Heat Equation ⋮ On extensions of local Dirichlet forms ⋮ Harnack inequality for the Schrödinger problem relative to strongly local Riemannian \(p\)-homogeneous forms with a potential in the Kato class ⋮ Harnack inequality for harmonic functions relative to a nonlinear \(p\)-homogeneous Riemannian Dirichlet form ⋮ Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory ⋮ Heat kernel generated frames in the setting of Dirichlet spaces ⋮ Unnamed Item ⋮ The diffusion phenomenon for dissipative wave equations in metric measure spaces ⋮ Heat kernel estimates and parabolic Harnack inequalities for symmetric Dirichlet forms ⋮ A topological splitting theorem for weighted Alexandrov spaces ⋮ Heat kernel estimates and parabolic Harnack inequalities on graphs and resistance forms ⋮ Polyhedra as domains of harmonic maps ⋮ Estimates for capacities of nodal sets and polarity criteria in recurrent Dirichlet spaces ⋮ Lipschitz continuity of solutions of Poisson equations in metric measure spaces ⋮ Mosco-convergence and Wiener measures for conductive thin boundaries ⋮ Eigenfunction expansions for generators of Dirichlet forms ⋮ Sobolev Inequalities in Familiar and Unfamiliar Settings ⋮ A Universality Property of Sobolev Spaces in Metric Measure Spaces ⋮ Volume growth and escape rate of symmetric diffusion processes ⋮ The Liouville property of unbounded fractal layers ⋮ Gradient estimates for heat kernels and harmonic functions ⋮ Harmonic mappings between singular metric spaces ⋮ Axiomatic regularity on metric spaces ⋮ Stability of heat kernel estimates for symmetric non-local Dirichlet forms ⋮ Isometric immersions of RCD spaces ⋮ Harnack inequalities for fuchsian type weighted elliptic equations ⋮ Wave propagation speed on fractals ⋮ L^p -Liouville property for non-local operators ⋮ Heat kernel based decomposition of spaces of distributions in the framework of Dirichlet spaces ⋮ Subelliptic harmonic maps ⋮ Parabolic Harnack inequality for time-dependent non-symmetric Dirichlet forms ⋮ Lipschitz algebras and derivations. II: Exterior differentiation ⋮ Reconstructions of distances by energy forms ⋮ Relaxed Dirichlet problem for the subelliptic \(p\)-Laplacian ⋮ The Harnack inequality for a class of nonlocal parabolic equations ⋮ Liouville theorems based on symmetric diffusions ⋮ On the decomposition principle and a Persson type theorem for general regular Dirichlet forms ⋮ Sobolev-Orlicz imbeddings, weak compactness, and spectrum ⋮ Diffusion processes and heat kernels on metric spaces ⋮ Potential theory on Gromov hyperbolic spaces ⋮ From Sobolev inequality to doubling

Cites Work

• Balls and metrics defined by vector fields. I: Basic properties
• Fundamental solutions and geometry of the sum of squares of vector fields
• Fundamental solutions for second order subelliptic operators
• The Wiener test for degenerate elliptic equations
• Wiener criterion and potential estimates for obstacle problems relative to degenerate elliptic operators
• Symmetric Markov processes
• Boundary theory for symmetric Markov processes
• Hypoelliptic differential operators and nilpotent groups
• Composite media and asymptotic Dirichlet forms
• The Poincaré inequality for vector fields satisfying Hörmander's condition
• Boundary value problems for some degenerate-elliptic operators
• Analyse harmonique non-commutative sur certains espaces homogènes. Etude de certaines intégrales singulières. (Non-commutative harmonic analysis on certain homogeneous spaces. Study of certain singular integrals.)
• DIRICHLET SPACES
• An embedding theorem for sobolev spaces related to non-smooth vector fieldsand harnack inequality
• On Harnack's theorem for elliptic differential equations
• The local regularity of solutions of degenerate elliptic equations
• Inequalities for the maximal function relative to a metric
• Elliptic Partial Differential Equations of Second Order
• Mesures associées à une forme de Dirichlet. Applications
• Degenerate elliptic‐parabolic equations of second order
• 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

This page was built for publication: A Saint-Venant type principle for Dirichlet forms on discontinuous media