Regularity for elliptic pairs over
Regularity for entropy solutions of a class of parabolic equations with irregular data
Using as a main tool the time-regularizing convolution operator introduced by R. Landes, we obtain regularity results for entropy solutions of a class of parabolic equations with irregular data. The results are obtained in a very general setting and include known previous results.
Regularity for entropy solutions of parabolic p-Laplacian type equations.
In this note we give some summability results for entropy solutions of the nonlinear parabolic equation ut - div ap (x, ∇u) = f in ] 0,T [xΩ with initial datum in L1(Ω) and assuming Dirichlet's boundary condition, where ap(.,.) is a Carathéodory function satisfying the classical Leray-Lions hypotheses, f ∈ L1 (]0,T[xΩ) and Ω is a domain in RN. We find spaces of type Lr(0,T;Mq(Ω)) containing the entropy solution and its gradient. We also include some summability results when f = 0 and the p-Laplacian...
Regularity for nonlinear elliptic systems of second order
Regularity for non-uniformly elliptic systems and application to some variational integrals.
Regularity for Signorini's Problem in linear eleasticity.
Regularity for solutions to the Navier-Stokes equations with one velocity component regular.
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 kinetic formulations via averaging lemmas
We present a new class of averaging lemmas directly motivated by the question of regularity for different nonlinear equations or variational problems which admit a kinetic formulation. In particular they improve the known regularity for systems like in isentropic gas dynamics or in some variational problems arising in thin micromagnetic films. They also allow to obtain directly the best known regularizing effect in multidimensional scalar conservation laws. The new ingredient here is to use velocity...
Regularity in kinetic formulations via averaging lemmas
We present a new class of averaging lemmas directly motivated by the question of regularity for different nonlinear equations or variational problems which admit a kinetic formulation. In particular they improve the known regularity for systems like γ = 3 in isentropic gas dynamics or in some variational problems arising in thin micromagnetic films. They also allow to obtain directly the best known regularizing effect in multidimensional scalar conservation laws. The new ingredient here is to...
Regularity in Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients.
Regularity in Parabolic Phase Transition Problems.
Regularity of a free boundary with application to the Pompeiu problem.
Regularity of a Minimal Surface at its Free Boundary.
Regularity of solutions of the Hamilton-Jacobi equation
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 free boundaries in two dimensions