On the degree theory for densely defined mappings of class .
On the density of the range for some nonlinear operators
On the differentiability of solutions of quasilinear elliptic equations
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 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 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 degenerate real Monge Ampère equation.
On the dynamic behavior and stability of controlled connected Rayleigh beams under pointwise output feedback
We study the dynamic behavior and stability of two connected Rayleigh beams that are subject to, in addition to two sensors and two actuators applied at the joint point, one of the actuators also specially distributed along the beams. We show that with the distributed control employed, there is a set of generalized eigenfunctions of the closed-loop system, which forms a Riesz basis with parenthesis for the state space. Then both the spectrum-determined growth condition and exponential stability...
On the economical solution method for a system of linear algebraic equations.