Multiplicity results for a perturbed elliptic Neumann problem.
Multiplicity results for nonlinear elliptic equations.
Multiplicity results for -Laplacian with critical nonlinearity of concave-convex type and sign-changing weight functions.
Multiplicity results of positive radial solutions for -Laplacian problems in exterior domains.
Multipliers in Sobolev spaces and exact convergence rate estimates for the finite-difference schemes
In this paper we present some recent results concerning convergence rate estimates for finite-difference schemes approximating boundary-value problems. Special attention is given to the problem of minimal smoothness of coefficients in partial differential equations necessary for obtaining the results.
Multiscale expansion and numerical approximation for surface defects⋆
This paper is a survey of articles [5, 6, 8, 9, 13, 17, 18]. We are interested in the influence of small geometrical perturbations on the solution of elliptic problems. The cases of a single inclusion or several well-separated inclusions have been deeply studied. We recall here techniques to construct an asymptotic expansion. Then we consider moderately close inclusions, i.e. the distance between the inclusions tends to zero more slowly than their characteristic size. We provide a complete asymptotic...
Natural boundary value problems for weighted form laplacians
The four natural boundary problems for the weighted form Laplacians acting on polynomial differential forms in the -dimensional Euclidean ball are solved explicitly. Moreover, an algebraic algorithm for generating a solution from the boundary data is given in each case.
Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints
The goal of this paper is to prove the first and second order optimality conditions for some control problems governed by semilinear elliptic equations with pointwise control constraints and finitely many equality and inequality pointwise state constraints. To carry out the analysis we formulate a regularity assumption which is equivalent to the first order optimality conditions. Though the presence of pointwise state constraints leads to a discontinuous adjoint state, we prove that the optimal...
Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints
The goal of this paper is to prove the first and second order optimality conditions for some control problems governed by semilinear elliptic equations with pointwise control constraints and finitely many equality and inequality pointwise state constraints. To carry out the analysis we formulate a regularity assumption which is equivalent to the first order optimality conditions. Though the presence of pointwise state constraints leads to a discontinuous adjoint state, we prove that the optimal control...
Necessary conditions of existence for an elliptic equation with source term and measure data involving -Laplacian.
Neumann problem in a class of harmonic functions in domains with a piecewise-Lyapunov boundary.
Neumann-Neumann algorithms for spectral elements in three dimensions
Neumann-Neumann methods for vector field problems.
New mixed finite volume methods for second order eliptic problems
In this paper we introduce and analyze new mixed finite volume methods for second order elliptic problems which are based on H(div)-conforming approximations for the vector variable and discontinuous approximations for the scalar variable. The discretization is fulfilled by combining the ideas of the traditional finite volume box method and the local discontinuous Galerkin method. We propose two different types of methods, called Methods I and II, and show that they have distinct advantages over...
Newton's Method for Convex Nonlinear Elliptic Boundary Value Problems.
Newton's Method for Gradient Equations Based upon the Fixed Point Map: Convergence and Complexity Study.
Non existence of bounded-energy solutions for some semilinear elliptic equations with a large parameter
Non résonance près de la première valeur propie d'un système elliptique quasilinéaire de type potentiel.
Noncoercive boundary value problems for the Lapace equation with a spectral parameter.
Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations
The paper deals with error estimates and lower bound approximations of the Steklov eigenvalue problems on convex or concave domains by nonconforming finite element methods. We consider four types of nonconforming finite elements: Crouzeix-Raviart, , and enriched Crouzeix-Raviart. We first derive error estimates for the nonconforming finite element approximations of the Steklov eigenvalue problem and then give the analysis of lower bound approximations. Some numerical results are presented to...