Annealed estimates on the Green function

DOI10.1007/s00440-014-0598-0zbMath1342.60101arXiv1304.4408OpenAlexW2085186189MaRDI QIDQ892160

Daniel Marahrens, Felix Otto

Publication date: 18 November 2015

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.4408

zbMATH Keywords

elliptic equationsGreen functionstochastic homogenizationannealed estimates

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) Random operators and equations (aspects of stochastic analysis) (60H25) Difference operators (39A70) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Green's functions for elliptic equations (35J08)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Noise-stability and central limit theorems for effective resistance of random electric networks
• Annealed estimates on the Green functions and uncertainty quantification
• Normal approximation for a random elliptic equation
• An optimal variance estimate in stochastic homogenization of discrete elliptic equations
• Disorder, entropy and harmonic functions
• Upper bounds for symmetric Markov transition functions
• The logarithmic Sobolev inequality for discrete spin systems on a lattice
• On homogenization of elliptic equations with random coefficients
• Green's function for elliptic systems: existence and Delmotte-Deuschel bounds
• A central limit theorem for the effective conductance: linear boundary data and small ellipticity contrasts
• Quantification of ergodicity in stochastic homogenization: optimal bounds via spectral gap on Glauber dynamics
• The free Markoff field
• On homogenization and scaling limit of some gradient perturbations of a massless free field
• On estimating the derivatives of symmetric diffusions in stationary random environment, with applications to \(\nabla\varphi\) interface model
• An optimal quantitative two-scale expansion in stochastic homogenization of discrete elliptic equations
• Inégalité de Harnack elliptique sur les graphes
• Continuity of Solutions of Parabolic and Elliptic Equations
• Random Walk: A Modern Introduction
• Logarithmic Sobolev Inequalities
• Séminaire de Probabilités XXXVI
• Fluctuation of Solutions to Linear Elliptic Equations with Noisy Diffusion Coefficients
• Uniqueness and maximal regularity for nonlinear elliptic systems of n--Laplace type with measure valued right hand side
• Partially Alternate Derivation of a Result of Nelson