-regularity of the Aronsson equation in
convergence of minimizers of a Ginzburg-Landau functional.
local regularity for the solutions of the -Laplacian on the Heisenberg group. The case
We prove the Hölder continuity of the homogeneous gradient of the weak solutions of the p-Laplacian on the Heisenberg group , for .
regularity of solutions of a quasilinear equation related to the Levi operator
Capacitary strong type estimates in semilinear problems
We prove the equivalence of various capacitary strong type estimates. Some of them appear in the characterization of the measures that are admissible data for the existence of solutions to semilinear elliptic problems with power growth. Other estimates are known to characterize the measures for which the Sobolev space can be imbedded into . The motivation comes from the semilinear problems: simpler descriptions of admissible data are given. The proof surprisingly involves the theory of singular...
Characterizations of p-superharmonic functions on metric spaces
We show the equivalence of some different definitions of p-superharmonic functions given in the literature. We also provide several other characterizations of p-superharmonicity. This is done in complete metric spaces equipped with a doubling measure and supporting a Poincaré inequality. There are many examples of such spaces. A new one given here is the union of a line (with the one-dimensional Lebesgue measure) and a triangle (with a two-dimensional weighted Lebesgue measure). Our results also...
Characterizations of the ranges of some nonlinear operators and applications to boundary value problems
Classical boundary value problems for Monge-Ampère type equations
Classical solution to a second order nonlinear elliptic system in
Classical Solutions of Nonlinear Schrödinger Equations.
Codazzi tensors and equations of Monge-Ampère type on compact manifolds of constant sectional curvature.
Compact embedding of a degenerate Sobolev space and existence of entire solutions to a semilinear equation for a Grushin-type operator
Compacteness methods for certain degenerate elliptic systems.
Compactness and global estimates for the geometric Paneitz equation in high dimensions.
Compactness of conformal metrics with positive gaussian curvature in
Comparison principle and Liouville type results for singular fully nonlinear operators
Comparison results for Hessian equations via symmetrization
Comparison results for semilinear elliptic equations via Picone-type identities.
Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results
Complex Ginzburg-Landau equations in high dimensions and codimension two area minimizing currents
There is an obvious topological obstruction for a finite energy unimodular harmonic extension of a -valued function defined on the boundary of a bounded regular domain of . When such extensions do not exist, we use the Ginzburg-Landau relaxation procedure. We prove that, up to a subsequence, a sequence of Ginzburg-Landau minimizers, as the coupling parameter tends to infinity, converges to a unimodular harmonic map away from a codimension-2 minimal current minimizing the area within the homology...