Regularity and free boundary regularity for the Laplacian in Lipschitz and domains.
Regularity and Uniqueness of Solutions to Boundary Blow-up Problems for the Complex Monge-Ampère Operator
We prove that plurisubharmonic solutions to certain boundary blow-up problems for the complex Monge-Ampère operator are Lipschitz continuous. We also prove that in certain cases these solutions are unique.
Regularity at infinity for a mixed problem for degenerate elliptic operators in a half-cylinder.
Regularity for a clamped grid equation on a domain with a corner.
Regularity for degenerate elliptic problems via p-harmonic approximation
Regularity for nonlinear elliptic systems of second order
Regularity for non-uniformly elliptic systems and application to some variational integrals.
Regularity for vector valued minimizers of some anisotropic integral functionals.
Regularity in elliptic free boundary problems. II. Equations of higher order
Regularity in free boundary problems
Regularity in Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients.
Regularity of a free boundary with application to the Pompeiu problem.
Regularity of differential forms minimizing degenerate elliptic functionals.
Regularity of domains of parameterized families of closed linear operators
The purpose of this paper is to provide a method of reduction of some problems concerning families of linear operators with domains to a problem in which all the operators have the same domain . To do it we propose to construct a family of automorphisms of a given Banach space X having two properties: (i) the mapping is sufficiently regular and (ii) for t ∈ . Three effective constructions are presented: for elliptic operators of second order with the Robin boundary condition with a parameter;...
Regularity of Lipschitz free boundaries for the thin one-phase problem
We study regularity properties of the free boundary for the thin one-phase problem which consists of minimizing the energy functional among all functions which are fixed on .
Regularity of minima: an invitation to the Dark Side of the Calculus of Variations
I am presenting a survey of regularity results for both minima of variational integrals, and solutions to non-linear elliptic, and sometimes parabolic, systems of partial differential equations. I will try to take the reader to the Dark Side...
Regularity of minima of variational integrals
Regularity of minimizers for a class of membrane energies
Regularity of optimal shapes for the Dirichlet’s energy with volume constraint
In this paper, we prove some regularity results for the boundary of an open subset of which minimizes the Dirichlet’s energy among all open subsets with prescribed volume. In particular we show that, when the volume constraint is “saturated”, the reduced boundary of the optimal shape (and even the whole boundary in dimension 2) is regular if the state function is nonnegative.
Regularity of optimal shapes for the Dirichlet's energy with volume constraint
In this paper, we prove some regularity results for the boundary of an open subset of which minimizes the Dirichlet's energy among all open subsets with prescribed volume. In particular we show that, when the volume constraint is “saturated”, the reduced boundary of the optimal shape (and even the whole boundary in dimension 2) is regular if the state function is nonnegative.