We study generalized Robin boundary conditions, Robin-to-Dirichlet maps, and Kreintype resolvent formulas for Schrödinger operators on bounded Lipschitz domains in R, n > 2. We also discuss the case of bounded C-domains, (1/2) < r < 1.

Sufficient conditions are obtained so that a weak subsolution of (0.1), bounded from above on the parabolic boundary of the cylinder Q, turns out to be bounded from above in Q.

We consider the stability in the inverse problem consisting in the determination of an electric potential q, appearing in a Dirichlet initial-boundary value problem for the wave equation ∂2 t u − ∆u + q(x)u = 0 in an unbounded wave guide Ω = ω × R with ω a bounded smooth domain of R2, from boundary observations. The observation is given by the Dirichlet to Neumann map associated to a wave equat...

Let R 2 be a bounded domain with Lipschitz boundary and let : ! R be a function which is measurable and bounded away from zero and innnity. We consider the divergence form elliptic operator

In this article we study holomorphic isometries of the Poincaré disk into bounded symmetric domains. Earlier we solved the problem of analytic continuation of germs of holomorphic maps between bounded domains which are isometries up to normalizing constants with respect to the Bergman metric, showing in particular that the graph V0 of any germ of holomorphic isometry of the Poincaré disk ∆ into...

In this article we study holomorphic isometries of the Poincaré disk into bounded symmetric domains. Earlier we solved the problem of analytic continuation of germs of holomorphic maps between bounded domains which are isometries up to normalizing constants with respect to the Bergman metric, showing in particular that the graph V0 of any germ of holomorphic isometry of the Poincaré disk ∆ into...

Siegel disks are domains around fixed points of holomorphic maps in which the maps are locally linearizable (i.e., become a rotation under an appropriate change of coordinates which is analytic in a neighborhood of the origin). The dynamical behavior of the iterates of the map on the boundary of the Siegel disk exhibits strong scaling properties which have been intensively studied in the physic...

Here D ⊂ R is a bounded domain with Lipschitz boundary ΓD, E is the electric field, H is the magnetic field, x̂ = x/|x|, and n is the unit outer normal to ΓD. The applied current J and the initial conditions E0,H0 are assumed to be supported in the circle BR = {x ∈ R : |x| < R} for some R > 0. The electric permittivity ε and magnetic permeability μ are assumed to be positive constants. We remark...

This paper is concerned with homeomorphisms of Euclidean spaces onto themselves, with bounded orbits. The following results are obtained. (1) A homeomorphism of E onto itself has both bounded orbits and an equicontinuous family of iterates iff it is a conjugate of either a rotation or a reflection; (2) An example of Bing is modified to produce a fixed point free, orientation preserving homeomor...

in this paper, we investigate the existence of positive solutions for the ellipticequation $delta^{2},u+c(x)u = lambda f(u)$ on a bounded smooth domain $omega$ of $r^{n}$, $ngeq2$, with navier boundary conditions. we show that there exists an extremal parameter$lambda^{ast}>0$ such that for $lambda< lambda^{ast}$, the above problem has a regular solution butfor $lambda> lambda^{ast}$, the probl...