Vy Khoi Le

Moment theory and some inverse problems in potential theory and heat conduction

Introduction.- Mathematical Preliminaries.- Regularization of moment problems by trancated expansion and by the Tikhonov method.- Backus-Gilbert regularization of a moment problem.- The Hausdorff moment problem: regularization and error estimates.- Analytic functions: reconstruction and Sinc approximations.- Regularization of some inverse problems in potential theory.- Regularization of some inverse problems in heat conduction.- Epilogue.- References.- Index.

Minimization problems for noncoercive functionals subject to constraints

We consider noncoercive functionals on a reflexive Banach space and establish minimization theorems for such functionals on smooth constraint manifolds. These results in turn yield critical point theorems for certain classes of homogeneous functionals. Several applications to the study of boundary value problems for quasilinear elliptic equations are included.

Some Existence Results on Nontrivial Solutions of the Prescribed Mean Curvature Equation

Abstract The paper is concerned with an eigenvalue problem for the prescribed mean curvature equation. We formulate the problem as a variational inequality and show that under some growth conditions on the lower order term, the relaxed problem has at least two nontrivial solutions in a space of functions of bounded variation when the parameter is small.

On a non-smooth eigenvalue problem in Orlicz–Sobolev spaces

This article studies a non-smooth eigenvalue problem for a Dirichlet boundary value inclusion on a bounded domain Ω which involves a φ-Laplacian and the generalized gradient in the sense of Clarke of a locally Lipschitz function depending also on the points in Ω. Specifically, the existence of a sequence of eigensolutions satisfying in addition certain asymptotic and locational properties is established. The approach relies on an approximation process in a suitable Orlicz–Sobolev space by eigenvalue problems in finite-dimensional spaces for which one can apply a finite-dimensional, non-smooth version of the Ljusternik–Schnirelman theorem. As a byproduct of our analysis, a version of Aubin–Clarkes theorem in Orlicz spaces is obtained.

Multiple Solutions for Quasilinear Elliptic Neumann Problems in Orlicz-Sobolev Spaces

We investigate the existence of multiple solutions to quasilinear elliptic problems containing Laplace like operators (-Laplacians). We are interested in Neumann boundary value problems and our main tool is Brézis-Nirenbergs local linking theorem.

A global bifurcation result for quasilinear elliptic equations in Orlicz-Sobolev spaces

The paper is concerned with a global bifurcation result for the equation

On second order elliptic equations and variational inequalities with anisotropic principal operators

-\text{div} (A(|\nabla u|) \nabla u) = g(x,u,\lambda)

Existence results for hemivariational inequalities with measures

in a general domain