Regularity of solutions to a one dimensional plasticity model
Regularity of solutions to doubly nonlinear diffusion equations.
Regularity of solutions to the Navier-Stokes equation.
Regularity of some nonlinear quantities on superharmonic functions in local Herz-type Hardy spaces.
In this paper, the authors introduce a kind of local Hardy spaces in Rn associated with the local Herz spaces. Then the authors investigate the regularity in these local Hardy spaces of some nonlinear quantities on superharmonic functions on R2. The main results of the authors extend the corresponding results of Evans and Müller in a recent paper.
Regularity of stable solutions of -Laplace equations through geometric Sobolev type inequalities
We prove a Sobolev and a Morrey type inequality involving the mean curvature and the tangential gradient with respect to the level sets of the function that appears in the inequalities. Then, as an application, we establish a priori estimates for semistable solutions of in a smooth bounded domain . In particular, we obtain new and bounds for the extremal solution when the domain is strictly convex. More precisely, we prove that if and if .
Regularity of the Poisson kernel and free boundary problems
Regularity of the solution of some transmission problems in domains with cuspidal point
Regularity results for transmission problems in domains with (outgoing) cuspidal points are considered. We prove in some special but generic situations that the solution is piecewise in .
Regularity of the solution of the first initial-boundary value problem for hyperbolic equations in domains with cuspidal points on boundary.
Regularity of the solutions for a Robin problem and some applications.
Regularity of the solutions of elliptic systems in polyhedral domains.
Regularity of the solutions of second order evolution equations and their attractors
Regularity of weak solutions for a class of infintely degenerate elliptic semilinear equation
Regularity of weak solutions of the Navier-Stokes equations near the smooth boundary.
Regularity of weak solutions to the magneto-hydrodynamics equations in terms of the direction of velocity.
Regularity of weakly well-posed characteristic boundary value problems.
Regularity problem for one class of nonlinear parabolic systems with non-smooth in time principal matrices
Partial regularity of solutions to a class of second order nonlinear parabolic systems with non-smooth in time principal matrices is proved in the paper. The coefficients are assumed to be measurable and bounded in the time variable and VMO-smooth in the space variables uniformly with respect to time. To prove the result, we apply the so-called -caloric approximation method. The method was applied by the authors earlier to study regularity of quasilinear systems.
Regularity properties of semilinear boundary problems in Besov and Triebel-Lizorkin spaces
Regularity properties of solutions of elliptic equations in in limit cases
In this paper the Dirichlet problem for a linear elliptic equation in an open, bounded subset of is studied. Regularity properties of the solutions are proved, when the data are -functions or Radon measures. In particular sharp assumptions which guarantee the continuity of solutions are given.
Regularity properties of the attractor to the Navier-Stokes equations
Existence of a global attractor for the Navier-Stokes equations describing the motion of an incompressible viscous fluid in a cylindrical pipe has been shown already. In this paper we prove the higher regularity of the attractor.
Regularity results for a class of quasiconvex functionals with nonstandard growth