Related papers: Regularity Results for Generalized Electro-Magneti…
A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all…
We establish existence and uniqueness of generalized solutions to the initial-boundary value problem corresponding to an Euler-Bernoulli beam model from mechanics. The governing partial differential equation is of order four and involves…
We prove the unique solvability in weighted Sobolev spaces of non-divergence form elliptic and parabolic equations on a half space with the homogeneous Neumann boundary condition. All the leading coefficients are assumed to be only…
About thirty years ago we looked for "minimal assumptions" on the data which guarantee that solutions to the $\,2-D\,$ evolution Euler equations in a bounded domain are classical. Classical means here that all the derivatives appearing in…
An inverse problem of identifying locations and certain properties of small dielectric inhomogeneities in a homogeneous background medium from boundary measurements on a part of the boundary is studied. Using as weights particular…
The existence of ground states and (multiple) bound states to semilinear time-independent Maxwell and Schr\"odinger equations, with or without $L^2$-constraints, is investigated.
We consider two inverse boundary value problems for the time-harmonic Maxwell equations in an infinite slab. Assuming that tangential boundary data for the electric and magnetic fields at a fixed frequency is available either on subsets of…
In this paper, we study the regularity of solutions to uniformly degenerate elliptic equations in bounded domains under the condition that the characteristic polynomials have varying characteristic exponents.
In this paper, we analyze nonlinear differential equations subject to generalized boundary conditions. More specifically, we provide a framework from which we can provide conditions, which are straightforward to check, for the solvability…
The time-harmonic Maxwell equations at high wavenumber k in domains with an analytic boundary and impedance boundary conditions are considered. A wavenumber-explicit stability and regularity theory is developed that decomposes the solution…
Regularity theorems \`a la Avellaneda-Lin are an indispensable part of the modern quantitative theory of stochastic homogenization. While interior regularity results for random elliptic operators have been available for a while, on general…
The paper studies some inverse boundary value problem for simplest parabolic equations such that the homogenuous Cauchy condition is ill posed at initial time. Some regularity of the solution is established for a wide class of boundary…
We consider the regularity of stationary solutions to the linearized Boltzmann equations in bounded $C^1$ convex domains in $\mathbb{R}^3$ for gases with cutoff hard potential and cutoff Maxwellian gases. We prove that the stationary…
In this article we establish fine results on the boundary behavior of solutions to nonlocal equations in $C^{k,\gamma}$ domains which satisfy local Neumann conditions on the boundary. Such solutions typically blow up at the boundary like $v…
We investigate the properties of a fairly large class of boundary conditions for the linearised Einstein equations in the Riemannian setting, ones which generalise the linearised counterpart of boundary conditions proposed by Anderson.…
We prove an existence theorem for positive solutions to Lichnerowicz-type equations on complete manifolds with boundary and nonlinear Neumann conditions. This kind of nonlinear problems arise quite naturally in the study of solutions for…
We analyze the stability of Maxwell equations in bounded domains taking into account electric and magnetization effects. Well-posedness of the model is obtained by means of semigroup theory. A passitivity assumption guarantees the…
We study Maxwell's equations in time domain in an anisotropic medium. The goal of the paper is to solve an inverse boundary value problem for anisotropies characterized by scalar impedance $\alpha$. This means that the material is…
In this paper, we study the nonhomogeneous Dirichlet problem concerning general semilinear elliptic equations in divergence form. We establish that the boundary Lipschitz regularity of solutions under some more weaker conditions on the…
This paper presents an exterior-algebra generalization of electromagnetic fields and source currents as multivectors of grades $r$ and $r-1$ respectively in a flat space-time with $n$ space and $k$ time dimensions. Formulas for the Maxwell…