相关论文: Perturbation of Domain: Ordinary Differential Equa…

In this paper we study some boundary value problems for a fractional analogue of second order elliptic equation with an involution perturbation in a rectangular domain. Theorems on existence and uniqueness of a solution of the considered…

We continue the analysis started in [Noris,Terracini,Indiana Univ Math J,2010] and [Bonnaillie-No\"el,Noris,Nys,Terracini,Analysis & PDE,2014], concerning the behavior of the eigenvalues of a magnetic Schr\"odinger operator of Aharonov-Bohm…

This survey is devoted to discussing the problems of the unique determination of surfaces that are the boundaries of (generally speaking) nonconvex domains. First (in Sec. 2) we examine some results on the problem of the unique…

This paper is concerned with a Neumann type problem for singularly perturbed fractional nonlinear Schr\"odinger equations with subcritical exponent. For some smooth bounded domain $\Omega\subset \mathbf R^n$, our boundary condition is given…

In this paper we begin exploring a local regularity theory for elliptic equations having coefficients which are degenerate or singular on some lower dimensional manifold $$ -\mathrm{div}(|y|^aA(x,y)\nabla…

The Derivative Nonlinear Schr\"odinger equation is an $L^2$-critical nonlinear dispersive equation model for Alfv\'en waves in space plasmas. Recent numerical studies on an $L^2$-supercritical extension of this equation provide evidence of…

The effect of the small dispersion on the self-focusing of solutions of the equations of nonlinear geometric optics in one-dimensional case is investigated. In the main order this influence is described by means of the universal special…

The aim of this paper is to provide uniform estimates for the eigenvalue spacings of one-dimensional semiclassical Schr\"odinger operators with singular potentials on the half-line. We introduce a new development of semiclassical measures…

We obtain bounds on the complex eigenvalues of non-self-adjoint Schr\"odinger operators with complex potentials, and also on the complex resonances of self-adjoint Schr\"odinger operators. Our bounds are compared with numerical results, and…

We prove Strichartz estimates with a loss of derivatives for the Schr\"odinger equation on polygonal domains with either Dirichlet or Neumann homogeneous boundary conditions. Using a standard doubling procedure, estimates the on polygon…

A Rayleigh-Schrodinger type of perturbation scheme is employed to study weak self-interacting scalar potential perturbations occurring in scalar field models describing 1D domain kinks and 3D domain walls. The solutions for the unperturbed…

Operator splitting methods combined with finite element spatial discretizations are studied for time-dependent nonlinear Schr\"odinger equations. In particular, the Schr\"odinger-Poisson equation under homogeneous Dirichlet boundary…

We give lower bounds for the first Dirichilet eigenvalues for domains in submanifolds with locally bounded mean curvatures. These bounds depend on the injectivity radius, sectional curvature (upperbound) of the ambient space and on the mean…

For Schr\"odinger operators $H_V=-\Delta_g+V$ with critically singular potentials $V$ on compact manifolds, we prove sharp estimates for the restriction of eigenfunctions to submanifolds. Our method refines the perturbative argument by…

When a strict local martingale is projected onto a subfiltration to which it is not adapted, the local martingale property may be lost, and the finite variation part of the projection may have singular paths. This phenomenon has…

We study the higher-order fractional Schr\"odinger equation with local nonlinear perturbations and investigate both the forward and inverse problems. We establish both the Sobolev $H^s$ and H\"older $C^s$ estimates for the well-posedness of…

I present an example of a discrete Schr"odinger operator that shows that it is possible to have embedded singular spectrum and, at the same time, discrete eigenvalues that approach the edges of the essential spectrum (much) faster than…

We consider singular perturbed eigenvalue problem for Laplace operator in a two-dimensional domain. In the boundary we select a set depending on a character small parameter and consisting of a great number of small disjoint parts. On this…

Proximity effect systems in superconducting films can be modeled by a one-dimensional Schr\"odinger equation. Several systems are studied using Dirichlet and Neumann boundary conditions. It is observed that the two boundary conditions have…

We derive spectral estimates of the Lieb-Thirring type for eigenvalues of Dirichlet Laplacians on strictly shrinking spiral-shaped domains.