On the differential system governing flows in magnetic field with data in .
On the diffraction of high-frequency waves by arbitrary shape cone. Neumann case
On the dimension of -harmonic measure.
On the dimension of -harmonic measure in space
Let , and let , be given. In this paper we study the dimension of -harmonic measures that arise from non-negative solutions to the -Laplace equation, vanishing on a portion of , in the setting of -Reifenberg flat domains. We prove, for , that there exists small such that if is a -Reifenberg flat domain with , then -harmonic measure is concentrated on a set of -finite -measure. We prove, for , that for sufficiently flat Wolff snowflakes the Hausdorff dimension of -harmonic measure...
On the dimension of the attractor for a perturbed 3d Ladyzhenskaya model
We consider the so-called Ladyzhenskaya model of incompressible fluid, with an additional artificial smoothing term ɛΔ3. We establish the global existence, uniqueness, and regularity of solutions. Finally, we show that there exists an exponential attractor, whose dimension we estimate in terms of the relevant physical quantities, independently of ɛ > 0.
On the dimension of the pullback attractors for -Navier-Stokes equations.
On the Dirac delta as initial condition for nonlinear Schrödinger equations
On the Dirichlet and Neumann problems in multi-dimensional cone
We consider an elliptic pseudodifferential equation in a multi-dimensional cone, and using the wave factorization concept for an elliptic symbol we describe a general solution of such equation in Sobolev-Slobodetskii spaces. This general solution depends on some arbitrary functions, their quantity being determined by an index of the wave factorization. For identifying these arbitrary functions one needs some additional conditions, for example, boundary conditions. Simple boundary value problems,...
On the Dirichlet boundary value problem for nonlinear elliptic partial differential equations in Sobolev power weight spaces
On the Dirichlet Probelm for Surfaces of Prescribed Mean Curvature.
On the Dirichlet problem associated with the Dunkl Laplacian
This paper deals with the questions of the existence and uniqueness of a solution to the Dirichlet problem associated with the Dunkl Laplacian as well as the hypoellipticity of on noninvariant open sets.
On the Dirichlet problem for a degenerate elliptic equation
On the Dirichlet problem for a second order elliptic system with degeneration on the entire domain boundary.
On the Dirichlet problem for fully nonlinear parabolic equations
On the Dirichlet problem for linear elliptic equations in plane domains with corners
On the Dirichlet problem for minimal graphs in hyperbolic space.
On the Dirichlet problem for nonlinear degenerate elliptic equations and applications to optimal control.
On the Dirichlet problem for quasilinear elliptic second order equations with triple degeneracy and singularity in a domain with a boundary conical point.
On the Dirichlet Problem for Semi-Linear Elliptic Equation with L2-Boundary Data.
On the Dirichlet Problem for the Complex Monge-Ampère Operator.