Regularity of minima: an invitation to the dark side of the calculus of variations
G Mingione - Applications of mathematics, 2006 - Springer
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Elliptic equations with BMO coefficients in Reifenberg domains
SS Byun, L Wang - … on Pure and Applied Mathematics: A …, 2004 - Wiley Online Library
The inhomogeneous Dirichlet problems concerning divergence form elliptic equations are
studied. Optimal regularity requirements on the coefficients and domains for the W1, p …
studied. Optimal regularity requirements on the coefficients and domains for the W1, p …
A local estimate for nonlinear equations with discontinuous coefficients
J Kinnunen, S Zhou - Communications in partial differential …, 1999 - Taylor & Francis
2044 KINNUNEN AND ZHOU for all (E Rn and almost every x E Q. Here X and A are posit,
ive constants and q.(denotes the standard inner product of v, Je Rn. Suppose that …
ive constants and q.(denotes the standard inner product of v, Je Rn. Suppose that …
Global estimates for quasilinear elliptic equations on Reifenberg flat domains
T Mengesha, NC Phuc - Archive for Rational Mechanics and Analysis, 2012 - Springer
New global regularity estimates are obtained for solutions to a class of quasilinear elliptic
boundary value problems. The coefficients are assumed to have small BMO seminorms, and …
boundary value problems. The coefficients are assumed to have small BMO seminorms, and …
Riesz transforms and elliptic PDEs with VMO coefficients
T Iwaniec, C Sbordone - Journal d'Analyse Mathématique, 1998 - Springer
The present paper is concerned with L p-theory of the uniformly elliptic differential operator
Lu= ∑ i, j ∂ ∂ x_i (a_ i, j (x) ∂ ∂ x_i\,) in R n with coefficients of vanishing mean oscillation …
Lu= ∑ i, j ∂ ∂ x_i (a_ i, j (x) ∂ ∂ x_i\,) in R n with coefficients of vanishing mean oscillation …
Bounds of Riesz Transforms on Spaces for Second Order Elliptic Operators
Z Shen - Annales de l'institut Fourier, 2005 - numdam.org
Under these assumptions, it is known that the Riesz transform∇(L)− 1/2 is bounded on Lp
(Ω) for 1< p< 2+ ε where ε= ε (n, µ)> 0, and is of weak type (1, 1)(see eg [4],[7]). Moreover, the …
(Ω) for 1< p< 2+ ε where ε= ε (n, µ)> 0, and is of weak type (1, 1)(see eg [4],[7]). Moreover, the …
Weighted and regularity estimates for nonlinear equations on Reifenberg flat domains
T Mengesha, NC Phuc - Journal of Differential Equations, 2011 - Elsevier
Global weighted Lp estimates are obtained for the gradient of solutions to nonlinear elliptic
Dirichlet boundary value problems over a bounded nonsmooth domain. Morrey and Hölder …
Dirichlet boundary value problems over a bounded nonsmooth domain. Morrey and Hölder …
Elliptic equations in divergence form with partially BMO coefficients
The solvability in Sobolev spaces is proved for divergence form second order elliptic
equations in the whole space, a half space, and a bounded Lipschitz domain. For equations …
equations in the whole space, a half space, and a bounded Lipschitz domain. For equations …
On the L p -Solvability of Higher Order Parabolic and Elliptic Systems with BMO Coefficients
We prove the solvability in Sobolev spaces for both divergence and non-divergence form
higher order parabolic and elliptic systems in the whole space, on a half space, and on a …
higher order parabolic and elliptic systems in the whole space, on a half space, and on a …
Improved Sobolev regularity for linear nonlocal equations with VMO coefficients
S Nowak - Mathematische Annalen, 2023 - Springer
This work is concerned with both higher integrability and differentiability for linear nonlocal
equations with possibly very irregular coefficients of VMO-type or even coefficients that are …
equations with possibly very irregular coefficients of VMO-type or even coefficients that are …