A remark on the note : “Partial Hölder continuity of the spatial derivatives of the solutions to nonlinear parabolic systems with quadratic growth”
A remark on the regularity for the 3D Navier-Stokes equations in terms of the two components of the velocity.
A short note on theory for Stokes problem with a pressure-dependent viscosity
We study higher local integrability of a weak solution to the steady Stokes problem. We consider the case of a pressure- and shear-rate-dependent viscosity, i.e., the elliptic part of the Stokes problem is assumed to be nonlinear and it depends on and on the symmetric part of a gradient of , namely, it is represented by a stress tensor which satisfies -growth condition with . In order to get the main result, we use Calderón-Zygmund theory and the method which was presented for example in...
A singular ODE related to quasilinear elliptic equations.
A sufficient condition for the well posedness of a Goursat problem
A system of nonlinear degenerate parabolic equations.
A temperature control problem.
A variational treatment for general elliptic equations of the flame propagation type : regularity of the free boundary
A W1,p-Estimate for Solutions to Mixed Boundary Value Problems for Second Order Elliptic Differential Equtions.
Abrupt and smooth separation of free boundaries in flow problems
Abstract linear hyperbolic equations and asymptotic equivalence as
Abstract Quasilinear Parabolic Equations.
Addendum to "Hölder estimates for nonlinear degenerate parabolic systems".
Additional note on partial regularity of weak solutions of the Navier-Stokes equations in the class
We present a simplified proof of a theorem proved recently concerning the number of singular points of weak solutions to the Navier-Stokes equations. If a weak solution belongs to , then the set of all possible singular points of in is at most finite at every time .
Additional regularity for Lipschitz solutions of PDE.
Almost classical solutions of Hamilton-Jacobi equations.
An approximate layering method for multi-dimensional nonlinear parabolic systems of a certain type
An Elementary Partial Regularity Proof for Vector-Valued Obstacle Problems.
An example of a nonlinear second order elliptic system in three dimension
We provide an explicit example of a nonlinear second order elliptic system of two equations in three dimension to compare two -regularity theories. We show that, for certain range of parameters, the theory developed in Daněček, Nonlinear Differential Equations Appl.9 (2002), gives a stronger result than the theory introduced in Koshelev, Lecture Notes in Mathematics,1614, 1995. In addition, there is a range of parameters where the first theory gives H"older continuity of solution for all , while...
An existence proof for the stationary compressible Stokes problem
In this paper, we prove the existence of a solution for a quite general stationary compressible Stokes problem including, in particular, gravity effects. The Equation Of State gives the pressure as an increasing superlinear function of the density. This existence result is obtained by passing to the limit on the solution of a viscous approximation of the continuity equation.