Related papers: Robin problem with measure data and singular nonli…
This paper examines inverse Cauchy problems that are governed by a kind of elliptic partial differential equation. The inverse problems involve recovering the missing data on an inaccessible boundary from the measured data on an accessible…
We analyze initial-boundary value problems for an integrable generalization of the nonlinear Schr\"odinger equation formulated on the half-line. In particular, we investigate the so-called linearizable boundary conditions, which in this…
We consider Laplace's equation in a periodically perforated domain with Robin boundary conditions on the holes, where the Robin coefficient is scaled proportionally to the inverse total surface area of the performations. We identify a…
In this paper, a class of linear parabolic systems of singularly perturbed second order differential equations of reaction-diffusion type with initial and Robin boundary conditions is considered. The components of the solution $\vec u$ of…
This work studies the initial-boundary value problem of the two-dimensional nonlinear Schr\"odinger equation on the half-plane with initial data in Sobolev spaces and Neumann or Robin boundary data in appropriate Bourgain spaces. It…
The present paper establishes that the Robin harmonic measure is quantitatively mutually absolutely continuous with respect to the surface measure on any Ahlfors regular set in any (quantifiably) connected domain for any elliptic operator.…
The standard approach to renormalization relies, technically, on the asymptotic perturbation of Gaussian measures embodied in Feynman diagram theory. From a mathematical standpoint this is not good enough, because thereby solving the…
In this paper we provide a comparison result between the solutions to the torsion problem for the Hermite operator with Robin boundary conditions and the one of a suitable symmetrized problem.
In this paper we address the uniqueness issue in the classical Robin inverse problem on a Lipschitz domain $\Omega\subset\RR^n$, with $L^\infty$ Robin coefficient, $L^2$ Neumann data and isotropic conductivity of class $W^{1,r}(\Omega)$,…
We analyze a splitting method for a canonical fluid structure interaction problem. The splittling method uses a Robin-Robin boundary condition, explicit strategy. We prove the method is stable and, furthermore, we provide an error estimate…
We revisit the problem of identifying an unknown portion of a boundary subject to a Robin condition based on a pair of Cauchy data on the accessible part of the boundary. It is known that a single measurement may correspond to infinitely…
We propose a novel non-compact, positivity-preserving scheme for linear non-divergence form elliptic equations. Based on the Feynman--Kac formula, the solution is represented as a conditional expectation associated with a diffusion…
In this article, we present a simpler and alternative proof of the solvability of the regularity problem - that is, the Dirichlet problem with boundary data in $\dot W^{1,p}$ - for uniformly elliptic operators on $\mathbb{R}^n_+$ under a…
In this paper we establish well posedness of the Neumann problem with boundary data in $L^2$ or the Sobolev space $\dot W^2_{-1}$, in the half space, for linear elliptic differential operators with coefficients that are constant in the…
We consider a semilinear elliptic equation with Dirichlet boundary conditions in a smooth, possibly unbounded, domain. Under suitable assumptions, we deduce a condition on the size of the domain that implies the existence of a positive…
In this paper, we prove two unique continuation results for second order elliptic equations with Robin boundary conditions on $C^{1,1}$ domains. The first one is a sharp vanishing order estimate of Robin problems with Lipschitz coefficients…
We consider a magnetic Schroedinger operator in a planar infinite strip with frequently and non-periodically alternating Dirichlet and Robin boundary conditions. Assuming that the homogenized boundary condition is the Dirichlet or the Robin…
Robin (or mixed) boundary conditions in quantum mechanics have received considerable attention in the last two decades, in particular, for applications to nanoscale systems. However, their utility has remained obscure to the larger physics…
In the current work we study a nonlocal parabolic problem with Robin boundary conditions. The problem arises from the study of an idealized electrically actuated MEMS (Micro-Electro-Mechanical System) device. Initially we study the…
We investigate singularly perturbed elliptic problems with multiplicative nonlocal diffusion terms subject to Robin boundary conditions. The diffusion depends on a global quantity of the solution, which introduces a nonlocal coupling…