Saddle Points and Multiple Solutions of Differential Equations.
Scattering problems in a domain with small holes.
In this paper, we consider a family of scattering problems in perforated unbounded domains Ωε. We assume that the perforation is contained in a bounded region and that the holes have a ?critical? size. We study the asymptotic behaviour of the outgoing solutions of the steady-state scattering problem and we prove that an extra term appears in the limit equation. Finally, we obtain convergence results for scattering frequencies and solutions.
Schéma des différences finies pour une équation non linéaire partielle du type elliptique avec dérivées mixtes
Schiffer problem and isoparametric hypersurfaces.
The Schiffer Problem as originally stated for Euclidean spaces (and later for some symmetric spaces) is the following: Given a bounded connected open set Ω with a regular boundary and such that the complement of its closure is connected, does the existence of a solution to the Overdetermined Neumann Problem (N) imply that Ω is a ball? The same question for the Overdetermined Dirichlet Problem (D). We consider the generalization of the Schiffer problem to an arbitrary Riemannian manifold and also...
Schouten tensor equations in conformal geometry with prescribed boundary metric.
Schwarz alternating and iterative refinemnt methods for mixed formulations of elliptic problems, part I: algorithms and numerical results.
Schwarz alternating and iterative refinemnt methods for mixed formulations of elliptic problems, part II: convergence theory.
Second-order boundary estimates for solutions to singular elliptic equations in borderline cases.
Semilinear elliptic boundary-value problems on bounded multiconnected domains.
Semilinear Elliptic Equations on Unbounded Domains.
Semilinear elliptic problems in unbounded domains
We investigate the existence of positive solutions and their continuous dependence on functional parameters for a semilinear Dirichlet problem. We discuss the case when the domain is unbounded and the nonlinearity is smooth and convex on a certain interval only.
Semilinear equations with exponential nonlinearity and measure data
Semilinear problems perturbed through the boundary condition
Shape and topological sensitivity analysis in domains with cracks
The framework for shape and topology sensitivity analysis in geometrical domains with cracks is established for elastic bodies in two spatial dimensions. The equilibrium problem for the elastic body with cracks is considered. Inequality type boundary conditions are prescribed at the crack faces providing a non-penetration between the crack faces. Modelling of such problems in two spatial dimensions is presented with all necessary details for further applications in shape optimization in structural...
Sharp maximum norm error estimates for general mixed finite element approximations to second order elliptic equations
Sign changing solutions for elliptic equations with critical growth in cylinder type domains
We prove the existence of positive and of nodal solutions for , , where and , for a class of open subsets of lying between two infinite cylinders.
Sign changing solutions for elliptic equations with critical growth in cylinder type domains
We prove the existence of positive and of nodal solutions for -Δu = |u|p-2u + µ|u|q-2u, , where µ > 0 and 2 < q < p = 2N(N - 2) , for a class of open subsets Ω of lying between two infinite cylinders.
Sign-changing solutions and multiplicity results for some quasi-linear elliptic Dirichlet problems
In this paper we show some results of multiplicity and existence of sign-changing solutions using a mountain pass theorem in ordered intervals, for a class of quasi-linear elliptic Dirichlet problems. As a by product we construct a special pseudo-gradient vector field and a negative pseudo-gradient flow for the nondifferentiable functional associated to our class of problems.
Sign-changing solutions for nonlinear elliptic problems depending on parameters.
Singular elliptic equations involving a concave term and critical Caffarelli-Kohn-Nirenberg exponent with sign-changing weight functions.