14,702 research outputs found
Nonlinear elliptic equations with high order singularities
We study non-variational degenerate elliptic equations with high order
singular structures. No boundary data are imposed and singularities occur along
an {\it a priori} unknown interior region. We prove that positive solutions
have a universal modulus of continuity that does not depend on their infimum
value. We further obtain sharp, quantitative regularity estimates for
non-negative limiting solutions.Comment: Revise
Sharp regularity for general Poisson equations with borderline sources
This article concerns optimal estimates for non-homogeneous degenerate
elliptic equation with source functions in borderline spaces of integrability.
We deliver sharp H\"older continuity estimates for solutions to -degenerate
elliptic equations in rough media with sources in the weak Lebesgue space
. For the borderline case, , solutions may not be bounded; nevertheless we
show that solutions have bounded mean oscillation, in particular
John-Nirenberg's exponential integrability estimates can be employed. All the
results presented in this paper are optimal. Our approach is based on powerful
Caffarelli-type compactness methods and it can be employed in a number order
situations.Comment: Review from previous version. Accepted for Publication: Journal de
Math\'ematiques Pures et Appliqu\'ee
Global Monge-Ampere equation with asymptotically periodic data
Let be a convex solution to in where is asymptotically close to a periodic function
. We prove that the difference between and a parabola is
asymptotically close to a periodic function at infinity, for dimension .Comment: 20 page
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