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Lipschitz Regularity for Elliptic Equations with Random Coefficients

, 2014
We develop a higher regularity theory for general quasilinear elliptic equations and systems in divergence form with random coefficients. The main result is a large-scale L∞-type estimate for the gradient of a solution.
S. Armstrong, J. Mourrat
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Elliptic Partial Differential Equations

Numerical Methods for Engineers and Scientists, 2018
M. Marin, A. Öchsner
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Nonlinear Singular Elliptic Equations

Journal of the London Mathematical Society, 1989
Let F be a dense vector subspace of a Banach space E, and f be a functional defined on F, in which f is not expected to have any critical point. We extend the variational theory to seek generalized critical points of f in E (not in F). Using these results we find solutions in \(W_ 0^{1,2}(\Omega)\) of the following equation \[ (P)\quad -\Delta u+c=Ke ...
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Elliptic Partial Differential Equations of Second Order

, 1997
P. Bassanini, A. Elcrat
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Strongly elliptic systems and boundary integral equations

Mathematical Gazette, 2000
M. Mudge
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Positive solutions of nonlinear elliptic equations involving critical sobolev exponents

, 1983
H. Brezis, L. Nirenberg
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Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I

, 1959
S. Agmon, A. Douglis, L. Nirenberg
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Nonlinear parabolic and elliptic equations

, 1993
C. Pao
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Colloidal Self-Assembly Approaches to Smart Nanostructured Materials

Chemical Reviews, 2022
Zhiwei Li Li, Yadong Yin
exaly