for some basis {ej}j=1 of R . We are interested in the spectral properties of the periodic SchrÃ¶dinger operator âˆ’âˆ†+ V(x) in R. When d = 3, L. Thomas [20] proved that the spectrum of âˆ’âˆ† + V is purelyâ€¦ (More)

Let L = âˆ’div(A(x)âˆ‡) be a second order elliptic operator with real, symmetric, bounded measurable coefficients on Rn or on a bounded Lipschitz domain subject to Dirichlet boundary condition. For anyâ€¦ (More)

In this paper we study the Lp boundary value problems for L(u) = 0 in R + , where L = âˆ’div(Aâˆ‡) is a second order elliptic operator with real and symmetric coefficients. Assume that A is periodic inâ€¦ (More)

Let be a bounded Lipschitz domain in n n â‰¥ 3 with connected boundary. We study the Robin boundary condition u/ N + bu = f âˆˆ L on for Laplaceâ€™s equation u = 0 in , where b is a non-negative functionâ€¦ (More)