Banach Spaces of Solutions of the Hemholtz Equation in the Plane.
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.
Bilinear representation formulas for polynominals.
Boundaries of graphs of harmonic functions.
Boundary augmented Lagrangian method for the Signorini problem
An augmented Lagrangian method, based on boundary variational formulations and fixed point method, is designed and analyzed for the Signorini problem of the Laplacian. Using the equivalence between Signorini boundary conditions and a fixed-point problem, we develop a new iterative algorithm that formulates the Signorini problem as a sequence of corresponding variational equations with the Steklov-Poincaré operator. Both theoretical results and numerical experiments show that the method presented...
Boundary behaviour of eigenfunctions of the Laplacian in a bi-tree.
Boundary integral equations and modified Green's functions
Boundary integral equations for mixed boundary value problems in polygonal domains and Galerkin approximation
Boundary integral equations of the logarithmic potential theory for domains with peaks
Integral equations of boundary value problems of the logarithmic potential theory for a plane domain with several peaks at the boundary are studied. We present theorems on the unique solvability and asymptotic representations for solutions near peaks. We also find kernels of the integral operators in a class of functions with a weak power singularity and describe classes of uniqueness.
Boundary mathematical problems in viscous liquid three-dimensional flows.
Boundary value problems and layer potentials on manifolds with cylindrical ends
We study the method of layer potentials for manifolds with boundary and cylindrical ends. The fact that the boundary is non-compact prevents us from using the standard characterization of Fredholm or compact pseudo-differential operators between Sobolev spaces, as, for example, in the works of Fabes-Jodeit-Lewis and Kral-Wedland . We first study the layer potentials depending on a parameter on compact manifolds. This then yields the invertibility of the relevant boundary integral operators in the...
Boundedness of the solution of the third problem for the Laplace equation
A necessary and sufficient condition for the boundedness of a solution of the third problem for the Laplace equation is given. As an application a similar result is given for the third problem for the Poisson equation on domains with Lipschitz boundary.
Bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals
We prove some new upper and lower bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals. In particular, we improve Pólya and Szegö's [Annals of Mathematical Studies 27 (1951)] lower bound for quadrilaterals and extend Hersch's [Z. Angew. Math. Phys. 17 (1966) 457–460] upper bound for parallelograms to general quadrilaterals.