On quasilinear elliptic equations in .
On Quasilinear Elliptic Systems of Diagonal Form.
On radial limit functions for entire solutions of second order elliptic equations in R2.
Given a homogeneous elliptic partial differential operator L of order two with constant complex coefficients in R2, we consider entire solutions of the equation Lu = 0 for whichlimr→∞ u(reiφ) =: U(eiφ)exists for all φ ∈ [0; 2π) as a finite limit in C. We characterize the possible "radial limit functions" U. This is an analog of the work of A. Roth for entire holomorphic functions. The results seems new even for harmonic functions.
On real interpolation, finite differences, and estimates depending on a parameter for discretizations of elliptic boundary value problems.
On reducing bandwidth of matrices in the Go-Away algorithm for regular grids.
On regularity of solutions to systems of partial differential equations which are locally close to elliptic systems of linear equations with constant coefficients. II.
On representations of real analytic functions by monogenic functions
Using the method of normalized systems of functions, we study one representation of real analytic functions by monogenic functions (i.e., solutions of Dirac equations), which is an Almansi’s formula of infinite order. As applications of the representation, we construct solutions of the inhomogeneous Dirac and poly-Dirac equations in Clifford analysis.
On Riesz means of eigenfunction expansions for the Kohn-Laplacian.
On semilinear elliptic eigenvalue problem with eigenparameter in the boundary conditions.
On shape and multiplicity of solutions for a singularly perturbed Neumann problem
We investigate the effect of the topology of the boundary ∂Ω and of the graph topology of the coefficient Q on the number of solutions of the nonlinear Neumann problem .
On shape optimization problems involving the fractional laplacian
Our concern is the computation of optimal shapes in problems involving (−Δ)1/2. We focus on the energy J(Ω) associated to the solution uΩ of the basic Dirichlet problem ( − Δ)1/2uΩ = 1 in Ω, u = 0 in Ωc. We show that regular minimizers Ω of this energy under a volume constraint are disks. Our proof goes through the explicit computation of the shape derivative (that seems to be completely new in the fractional context), and a refined adaptation of the moving plane method.
On shooting methods for the discrete Helmholtz equation with constant coefficients.
On Signorini problem for von Kármán equations
On Signorini problem for von Kármán equations. The case of angular domain
The paper deals with the generalized Signorini problem. The used method of pseudomonotone semicoercive operator inequality is introduced in the paper by O. John. The existence result for smooth domains from the paper by O. John is extended to technically significant "angular" domains. The crucial point of the proof is the estimation of the nonlinear term which appears in the operator form of the problem. The substantial technical difficulties connected with non-smoothness of the boundary are overcome...
On singular perturbation problems with Robin boundary condition
We consider the following singularly perturbed elliptic problemwhere satisfies some growth conditions, , and () is a smooth and bounded domain. The cases (Neumann problem) and (Dirichlet problem) have been studied by many authors in recent years. We show that, there exists a generic constant such that, as , the least energy solution has a spike near the boundary if , and has an interior spike near the innermost part of the domain if . Central to our study is the corresponding problem...
On solution of the integral equations for the potential problems of two circular-strips.
On solution to an optimal shape design problem in 3-dimensional linear magnetostatics
In this paper we present theoretical, computational, and practical aspects concerning 3-dimensional shape optimization governed by linear magnetostatics. The state solution is approximated by the finite element method using Nédélec elements on tetrahedra. Concerning optimization, the shape controls the interface between the air and the ferromagnetic parts while the whole domain is fixed. We prove the existence of an optimal shape. Then we state a finite element approximation to the optimization...
On solutions of the exterior Dirichlet problem for the minimal surface equation
On solutions of the Schrödinger equation with radiation conditions at infinity : the long-range case
We consider the homogeneous Schrödinger equation with a long-range potential and show that its solutions satisfying some a priori bound at infinity can asymptotically be expressed as a sum of incoming and outgoing distorted spherical waves. Coefficients of these waves are related by the scattering matrix. This generalizes a similar result obtained earlier in the short-range case.
On Solvability of a Nonlinear Elliptic Boundary Value Problem