Behavior of plane relaxation methods as multigrid smoothers.
Bernstein approximations of Dirichlet problems for elliptic operators on the plane.
Besov Regularity for Second Order Elliptic Boundary Value Problems with Variable Coefficients.
Best possible estimates of solutions to the transmission problem for the Laplace operator with N different media in a conical domain
We investigate the behavior of weak solutions to the transmission problem for the Laplace operator with N different media in a neighborhood of a boundary conical point. We establish a precise exponent of the decreasing rate of the solution.
Bifurcation of positive solutions for a semilinear equation with critical Sobolev exponent.
Borderline sharp estimates for solutions to Neumann problems.
Boundaries of graphs of harmonic functions.
Boundary estimates for solutions of Monge-Ampère equations in the plane
Boundary integral equations and modified Green's functions
Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume
In this paper we discuss the approximate reconstruction of inhomogeneities of small volume. The data used for the reconstruction consist of boundary integrals of the (observed) electromagnetic fields. The numerical algorithms discussed are based on highly accurate asymptotic formulae for the electromagnetic fields in the presence of small volume inhomogeneities.
Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume
In this paper we discuss the approximate reconstruction of inhomogeneities of small volume. The data used for the reconstruction consist of boundary integrals of the (observed) electromagnetic fields. The numerical algorithms discussed are based on highly accurate asymptotic formulae for the electromagnetic fields in the presence of small volume inhomogeneities.
Boundary Lagrange multipliers in finite element methods: error analysis in natural forms.
Boundary layers for transmission problems with singularities.
Boundary problems of the second order with an indefinite weight-function.
Boundary regularity for certain fully nonlinear elliptic equations.
Boundary Subspaces for the Finite Element Method With Lagrange Multipliers.
Boundary value problems for elliptic equations.
In this note I will describe some recent results, obtained jointly with R. Fefferman and J. Pipher [RF-K-P], on the Dirichlet problem for second-order, divergence form elliptic equations, and some work in progress with J. Pipher [K-P] on the corresponding results for the Neumann and regularity problems.
Boundary value problems for quasi-linear elliptic second order equations in unbounded cone-like domains
We study the behaviour of weak solutions (as well as their gradients) of boundary value problems for quasi-linear elliptic divergence equations in domains extending to infinity along a cone.
Boundary value problems for second order elliptic equations in unbounded domains and Saint-Venant's principle
Boundary value problems for second-order partial differential equations with operator coefficients.