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 results for a class of quasiconvex functionals with nonstandard growth
Regularity results for non-linear elliptic systems in two dimensions
Regularity results for parabolic systems related to a class of non-newtonian fluids
Regularity results for semilinear and geometric wave equations
Regularity results for vector fields of bounded distortion and applications.
Regularity theorems for solutions of partial differential equations for quasiconformal mappings in several dimensions [Book]
Regularity up to the boundary of solutions of the Dirichlet problem for certain degenerate elliptic equations.
Regularizing effects for multidimensional scalar conservation laws
Relative rearrangement on a finite measure space. Application to weighted spaces and to P.D.E.
Relative rearrangement on a finite measure space. Application to the regularity of weighted monotone rearrangement (Part I)
Remark on well-posedness and ill-posedness for the KdV equation.
Remarks about Signorini's problem in linear elasticity
Remarks on regularity criteria for the Navier-Stokes equations with axisymmetric data
We consider the axisymmetric Navier-Stokes equations with non-zero swirl component. By invoking the Hardy-Sobolev interpolation inequality, Hardy inequality and the theory of (1 < β < ∞) weights, we establish regularity criteria involving , or in some weighted Lebesgue spaces. This improves many previous results.