A free boundary problem for semilinear elliptic equations.
A free boundary problem for some modified predator-prey model in a higher dimensional environment
We focus on the free boundary problems for a Leslie-Gower predator-prey model with radial symmetry in a higher dimensional environment that is initially well populated by the prey. This free boundary problem is used to describe the spreading of a new introduced predator. We first establish that a spreading-vanishing dichotomy holds for this model. Namely, the predator either successfully spreads to the entire space as goes to infinity and survives in the new environment, or it fails to establish...
A free boundary problem for the -Laplacian: uniqueness, convexity, and successive approximation of solutions.
A free boundary value problem in potential theory
This paper is devoted to the formulation and solution of a free boundary problem for the Poisson equation in the plane. The object is to seek a domain and a function defined in satisfying the given differential equation together with both Dirichlet and Neumann type data on the boundary of . The Neumann data are given in a manner which permits reformulation of the problem as a variational inequality. Under suitable hypotheses about the given data, it is shown that there exists a unique solution...
A Fujita-type theorem for the Laplace equation with a dynamical boundary condition.
A full multigrid method for semilinear elliptic equation
A full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and semilinear problems on a very low dimensional space. The linearized boundary value problems are solved by some multigrid iterations. Besides the multigrid iteration, all other efficient numerical methods can also serve as...
A Galerkin procedure for approximating the flux on the boundary for elliptic and parabolic boundary value problems
A game interpretation of the Neumann problem for fully nonlinear parabolic and elliptic equations
We provide a deterministic-control-based interpretation for a broad class of fully nonlinear parabolic and elliptic PDEs with continuous Neumann boundary conditions in a smooth domain. We construct families of two-person games depending on a small parameter ε which extend those proposed by Kohn and Serfaty [21]. These new games treat a Neumann boundary condition by introducing some specific rules near the boundary. We show that the value function converges, in the viscosity sense, to the solution...
A general approach for multiconfiguration method sin quantum molecular chemistry
A general perturbation formula for electromagnetic fields in presence of low volume scatterers
In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields. This...
A general perturbation formula for electromagnetic fields in presence of low volume scatterers
In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields. This...
A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction
We establish an asymptotic representation formula for the steady state voltage perturbations caused by low volume fraction internal conductivity inhomogeneities. This formula generalizes and unifies earlier formulas derived for special geometries and distributions of inhomogeneities.
A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction
We establish an asymptotic representation formula for the steady state voltage perturbations caused by low volume fraction internal conductivity inhomogeneities. This formula generalizes and unifies earlier formulas derived for special geometries and distributions of inhomogeneities.
A generalization of Aubry-Mather theory to partial differential equations and pseudo-differential equations
A generalization of Ekeland's variational principle with applications.
A generalization of the Phragmén-Lindelöf principle for elliptic differential equations.
A generalization of the radiation condition of Sommerfeld for -body Schrödinger operators
A generalization of the saddle point method with applications
We show that one can drop an important hypothesis of the saddle point theorem without affecting the result. We then show how this leads to stronger results in applications.
A Generalization of the Schwarz Alternating Method to an Arbitrary Number of Subdomains.
A generalization related to Schrödinger operatorswith a singular potential.