Interior regularity for weak solutions of nonlinear second order elliptic systems
Interior regularity of weak solutions to the equations of a stationary motion of a non-Newtonian fluid with shear-dependent viscosity. The case
In this paper we consider weak solutions to the equations of stationary motion of a fluid with shear dependent viscosity in a bounded domain ( or ). For the critical case we prove the higher integrability of which forms the basis for applying the method of differences in order to get fractional differentiability of . From this we show the existence of second order weak derivatives of .
Interior regularity of weak solutions to the perturbed Navier-Stokes equations
In this paper we establish interior regularity for weak solutions and partial regularity for suitable weak solutions of the perturbed Navier-Stokes system, which can be regarded as generalizations of the results in L. Caffarelli, R. Kohn, L. Nirenberg: Partial regularity of suitable weak solutions of the Navier-Stokes equations, Commun. Pure. Appl. Math. 35 (1982), 771–831, and S. Takahashi, On interior regularity criteria for weak solutions of the Navier-Stokes equations, Manuscr. Math. 69...
Invariant measures and long-time behavior for the Benjamin-Ono equation
We summarize the main ideas in a series of papers ([20], [21], [22], [5]) devoted to the construction of invariant measures and to the long-time behavior of solutions of the periodic Benjamin-Ono equation.
Invertibility of some heat potentials in norms
Isoperimetric inequalities in parabolic equations
Kolmogorov Diameters in Solution Spaces of Systems of Partial Differential Equations.
-oценки решения задачи Коши для одномерного гиперболического уравнения высокого порядка с постоянными коэффициентами
-regularity of solutions to first initial-boundary value problem for hyperbolic equations in cusp domains.
regularity of velocity averages
L2-Integrability of Second Order Derivatives for Poisson's Equation in Nonsmooth Domains.
Le problème de la dérivée oblique non linéaire
L'equazione . Teorema di esistenza per un generale problema al contorno
Necessary and sufficient conditions are given for the existence of smooth solutions of the differential equations (1) with the boundary conditions (2). Coefficients of (1) and (2) are only supposed Hölder-continuous.
Les théorèmes de Leray et de Fujita-Kato pour le système de Boussinesq partiellement visqueux
Dans cet article, on étudie le système de Boussinesq décrivant le phénomène de convection dans un fluide incompressible et visqueux. Ce système est composé des équations de Navier-Stokes incompressibles avec un terme de force verticale dont l’amplitude est transportée sans dissipationpar le flot du champ de vitesses. On montre que les résultats classiques pour le système de Navier-Stokes standard demeurent vrais pour le système de Boussinesq bien qu’il n’y ait pas d’amortissement sur le terme de...
Levi equation for almost complex structures.
Linear Oblique Derivative Problems for the Uniformly Elliptic Hamilton-Jacobi-Bellman Equation.
Line-energy Ginzburg-Landau models : zero-energy states
We consider a class of two-dimensional Ginzburg-Landau problems which are characterized by energy density concentrations on a one-dimensional set. In this paper, we investigate the states of vanishing energy. We classify these zero-energy states in the whole space: They are either constant or a vortex. A bounded domain can sustain a zero-energy state only if the domain is a disk and the state a vortex. Our proof is based on specific entropies which lead to a kinetic formulation, and on a careful...
Liouville results for -Laplace equations of Lane-Emden-Fowler type
Liouville type condition and the interior regularity of quasilinear parabolic system (the case of BMO-solutions)
Lipschitz regularity for some asymptotically convex problems
We establish a local Lipschitz regularity result for local minimizers of asymptotically convex variational integrals.