On Hölder regularity for vector-valued minimizers of quasilinear functionals
We discuss the interior Hölder everywhere regularity for minimizers of quasilinear functionals of the type whose gradients belong to the Morrey space .
On homogeneizatìon problems for the Laplace operator in partially perforated domains with Neumann's condition on the boundary of cavities.
In this paper the problem of homogeneization for the Laplace operator in partially perforated domains with small cavities and the Neumann boundary conditions on the boundary of cavities is studied. The corresponding spectral problem is also considered.
On homogenization of non-divergence form partial difference equations.
On homogenization of solutions of boundary value problems in domains, perforated along manifolds
On identification of critical curves
The paper deals with the problem of finding a curve, going through the interior of the domain , accross which the flux , where is the solution of a mixed elliptic boundary value problem solved in , attains its maximum.
On infinitely many solutions of a semilinear elliptic eigenvalue problem
On interior and boundary regularity of weak solutions to a certain quasilinear elliptic system.
On Kelvin type transformation for Weinstein operator
The note develops results from [5] where an invariance under the Möbius transform mapping the upper halfplane onto itself of the Weinstein operator on is proved. In this note there is shown that in the cases , no other transforms of this kind exist and for case , all such transforms are described.
On Korn's second inequality
On -regularity for the gradient of a weak solution to nonlinear elliptic systems
Interior -regularity for the gradient of a weak solution to nonlinear second order elliptic systems is investigated.
On -estimates for solutions of elliptic boundary value problems
On Liouville theorem and apriori estimates for the scalar curvature equations
On Liouville theorem and Hölder continuity of weak solutions to some quasilinear elliptic systems of higher order
The aim of this paper is to show that the Liouville-type property is a sufficient and necessary condition for the regularity of weak solutions of quasilinear elliptic systems of higher orders.
On Liouville theorem and the regularity of weak solutions to some nonlinear elliptic systems of higher order
The aim of this paper is to show that Liouville type property is a sufficient and necessary condition for the regularity of weak solutions of nonlinear elliptic systems of the higher order.
On Liouville theorems, continuity and Hölder continuity of weak solutions to some quasilinear elliptic systems
On Liouville type theorems for second order elliptic differential equations
On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications
We study properties of Lipschitz truncations of Sobolev functions with constant and variable exponent. As non-trivial applications we use the Lipschitz truncations to provide a simplified proof of an existence result for incompressible power-law like fluids presented in [Frehse et al., SIAM J. Math. Anal34 (2003) 1064–1083]. We also establish new existence results to a class of incompressible electro-rheological fluids.
On local Lipschitz continuity of superposition operators
On localization of solutions of elliptic equations with nonhomogeneous anisotropic degeneracy.
On Lp estimates for square roots of second order elliptic operators on Rn.