In recent years, there has been a great deal of activity in the study of boundary value
problems with minimal smoothness assumptions on the coefficients or on the boundary of …

Time-dependent problems that are modeled by initial-boundary value problems for
parabolic or hyperbolic partial differential equations can be treated with the boundary …

We study the integral operators on the lateral boundary of a space-time cylinder that are
given by the boundary values and the normal derivatives of the single and double layer …

This paper presents two observability inequalities for the heat equation over×(0, T). In the
first one, the observation is from a subset of positive measure in×(0, T), while in the second …

We study boundary value problems for the time-harmonic form of the Maxwell equations, as
well as for other related systems of equations, on arbitrary Lipschitz domains in the three …

We consider the Lp-Neumann problem for the Schrödinger operator− Δ+ V in the region
above a Lipschitz graph. For 1< p≤ 2, it is shown that, under suitable conditions on the …

We consider boundary value problems for the heat equation in time-varying graph domains
of the form Ω={(x_0,x,t)∈R*R^n-1*R:x_0>A(x,t)\}, obtaining solvability of the Dirichlet and …

We are using d, u= Vu. v to denote the outer normal derivative on 8R. Note also that for
technical reasons explained below, we will consider the family of ecluatioits Atc-k2u= 0, k E …

We establish the L p resolvent estimates for the Stokes operator in Lipschitz domains in R^
d, d\geqq 3 for| 1 p-1 2|< 1 2d+ ε. The result implies that the Stokes operator in a three …

We use the method of layer potentials to study a transmission problem for the Helmholtz
equation in Lipschitz domains. Following the approach for the case of smooth interface, we …