On the smoothness of solutions of variational inequalities with obstacles
On the spatial analyticity of solutions to the Keller-Segel equations
The regularizing rate of solutions to the Keller-Segel equations in the whole space is estimated just as for the heat equation. As an application of these rate estimates, it is proved that the solution is analytic in spatial variables. Spatial analyticity implies that the propagation speed is infinite, i.e., the support of the solution coincides with the whole space for any short time, even if the support of the initial datum is compact.
On the Stefan problem: the variational approach and some applications
On the strongly damped wave equation and the heat equation with mixed boundary conditions.
On the two-phase membrane problem with coefficients below the Lipschitz threshold
On the -regularity of solutions to systems of differential equations in the case when the equations are constructed from discontinuous functions.
On three-dimensional vortex patches
On Two-Dimensional Elliptic Systems with a One-sided Condition.
On Two-Dimensional Quasi-Linear Elliptic Systems.
On weakly A-harmonic tensors
We study very weak solutions of an A-harmonic equation to show that they are in fact the usual solutions.
Ondes soniques
Optimal interior partial regularity for nonlinear elliptic systems for the case under natural growth condition.
Optimal regularity for codimension one minimal surfaces with a free boundary.
Optimal regularity for mixed parabolic problems in spaces of functions which are Hölder continuous with respect to space variables
Optimal regularity for quasilinear equations in stratified nilpotent Lie groups and applications.
Optimal regularity for the pseudo infinity Laplacian
In this paper we find the optimal regularity for viscosity solutions of the pseudo infinity Laplacian. We prove that the solutions are locally Lipschitz and show an example that proves that this result is optimal. We also show existence and uniqueness for the Dirichlet problem.
Optimal regularity of lower dimensional obstacle problems.
Optimal time and space regularity for solutions of degenerate differential equations
We derive optimal regularity, in both time and space, for solutions of the Cauchy problem related to a degenerate differential equation in a Banach space X. Our results exhibit a sort of prevalence for space regularity, in the sense that the higher is the order of regularity with respect to space, the lower is the corresponding order of regularity with respect to time.