Local regularity results for minima of anisotropic functionals and solutions of anisotropic equations.
Local Riesz transform characterization of local Hardy spaces
Local semiconvexity of Kantorovich potentials on non-compact manifolds
We prove that any Kantorovich potential for the cost function c = d2/2 on a Riemannian manifold (M, g) is locally semiconvex in the “region of interest”, without any compactness assumption on M, nor any assumption on its curvature. Such a region of interest is of full μ-measure as soon as the starting measure μ does not charge n – 1-dimensional rectifiable sets.
Local semiconvexity of Kantorovich potentials on non-compact manifolds*
We prove that any Kantorovich potential for the cost function c = d2/2 on a Riemannian manifold (M, g) is locally semiconvex in the “region of interest”, without any compactness assumption on M, nor any assumption on its curvature. Such a region of interest is of full μ-measure as soon as the starting measure μ does not charge n – 1-dimensional rectifiable sets.
Local smooth solution and non-relativistic limit of radiation hydrodynamics equations.
Local Smoothness of Weak Solutions to the Magnetohydrodynamics Equations via Blowup Methods
We demonstrate that there exist no self-similar solutions of the incompressible magnetohydrodynamics (MHD) equations in the space . This is a consequence of proving the local smoothness of weak solutions via blowup methods for weak solutions which are locally . We present the extension of the Escauriaza-Seregin-Sverak method to MHD systems.
Local solution for the Kadomtsev-Petviashvili equation with periodic conditions.
Local solution of Carrier's equation in a noncylindrical domain.
Local solution of parabolic equations with strongly increasing nonlinearity by the Rothe method
Local solutions for stochastic Navier Stokes equations
Local Solutions for Stochastic Navier Stokes Equations
In this article we consider local solutions for stochastic Navier Stokes equations, based on the approach of Von Wahl, for the deterministic case. We present several approaches of the concept, depending on the smoothness available. When smoothness is available, we can in someway reduce the stochastic equation to a deterministic one with a random parameter. In the general case, we mimic the concept of local solution for stochastic differential equations.
Local solvability and regularity results for a class of semilinear elliptic problems in nonsmooth domains
We consider a class of semilinear elliptic problems in two- and three-dimensional domains with conical points. We introduce Sobolev spaces with detached asymptotics generated by the asymptotical behaviour of solutions of corresponding linearized problems near conical boundary points. We show that the corresponding nonlinear operator acting between these spaces is Frechet differentiable. Applying the local invertibility theorem we prove that the solution of the semilinear problem has the same asymptotic...
Local solvability for semilinear partial differential equations of constant strength.
Local solvability of a constrained gradient system of total variation.
Local solvability of degenerate Monge-Ampère equations and applications to geometry.
Local solvability of diagonal semilinear parabolic systems
Local solvability of PDE with constant coefficients
Local solvability of some classes of linear and nonlinear partial differential equations.
Local stability of spike steady states in a simplified Gierer-Meinhardt system.
Local superconvergence analysis of the approximate boundary-flux calculation