A note on the Dirichlet problem for the elliptic linear operator in Sobolev spaces with weight
A note on the efficiency of residual-based a posteriori error estimators for some mixed finite element methods.
A note on the existence of two nontrivial solutions of a resonance problem.
A note on the moving hyperplane method.
A note on the Poisson-Boltzmann equation
A Note on the Problem -...u = ...u + u| u|2*-2.
A note on the regularity of the degenerate complex Monge-Ampère equation
We prove the almost regularity of the degenerate complex Monge-Ampère equation in a special case.
A note on the Rellich formula in Lipschitz domains.
Let L be a symmetric second order uniformly elliptic operator in divergence form acting in a bounded Lipschitz domain Ω of RN and having Lipschitz coefficients in Ω. It is shown that the Rellich formula with respect to Ω and L extends to all functions in the domain D = {u ∈ H01(Ω); L(u) ∈ L2(Ω)} of L. This answers a question of A. Chaïra and G. Lebeau.
A note on the Robin problem in potential theory (Preliminary communication)
A note on the shift theorem for the Laplacian in polygonal domains
We present a shift theorem for solutions of the Poisson equation in a finite planar cone (and hence also on plane polygons) for Dirichlet, Neumann, and mixed boundary conditions. The range in which the shift theorem holds depends on the angle of the cone. For the right endpoint of the range, the shift theorem is described in terms of Besov spaces rather than Sobolev spaces.
A note on the solvability of nonlinear elliptic problems with jumping nonlinearities
A Note on the Uniqueness and Structure of Solutions to the Dirichlet Problem for Some Elliptic Systems
In this note, we consider some elliptic systems on a smooth domain of . By using the maximum principle, we can get a more general and complete results of the identical property of positive solution pair, and thus classify the structure of all positive solutions depending on the nonlinarities easily.
A note on the variational structure of an elliptic system involving critical Sobolev exponent.
A note on two dimensional Bratu problem
A note on very weak -harmonic mappings.
A note on weighted estimates for the Schrödinger operator.
A numerical approach to a class of unilateral elliptic problems of non-variational type
A numerical minimization scheme for the complex Helmholtz equation
We use the work of Milton, Seppecher, and Bouchitté on variational principles for waves in lossy media to formulate a finite element method for solving the complex Helmholtz equation that is based entirely on minimization. In particular, this method results in a finite element matrix that is symmetric positive-definite and therefore simple iterative descent methods and preconditioning can be used to solve the resulting system of equations. We also derive an error bound for the method and illustrate...
A numerical minimization scheme for the complex Helmholtz equation
We use the work of Milton, Seppecher, and Bouchitté on variational principles for waves in lossy media to formulate a finite element method for solving the complex Helmholtz equation that is based entirely on minimization. In particular, this method results in a finite element matrix that is symmetric positive-definite and therefore simple iterative descent methods and preconditioning can be used to solve the resulting system of equations. We also derive an error bound for the method and illustrate...
A numerical solution using an adaptively preconditioned Lanczos method for a class of linear systems related with the fractional Poisson equation.