Oblique derivative problems and invariant measures
Oblique derivative problems for elliptic systems of second order equations in infinite domains.
Oblique derivative problems in Lipschitz domains: II. Discontinuous boundary data.
Observations on estimates for divergence elliptic equations with VMO coefficients
In this paper, we make some observations on the work of Di Fazio concerning estimates, , for solutions of elliptic equations , on a domain with Dirichlet data whenever and . We weaken the assumptions allowing real and complex non-symmetric operators and boundary. We also consider the corresponding inhomogeneous Neumann problem for which we prove the similar result. The main tool is an appropriate representation for the Green (and Neumann) function on the upper half space. We propose...
On a Bernoulli problem with geometric constraints
A Bernoulli free boundary problem with geometrical constraints is studied. The domain Ω is constrained to lie in the half space determined by x1 ≥ 0 and its boundary to contain a segment of the hyperplane {x1 = 0} where non-homogeneous Dirichlet conditions are imposed. We are then looking for the solution of a partial differential equation satisfying a Dirichlet and a Neumann boundary condition simultaneously on the free boundary. The existence and uniqueness of a solution have already been addressed...
On a Bernoulli problem with geometric constraints
A Bernoulli free boundary problem with geometrical constraints is studied. The domain Ω is constrained to lie in the half space determined by x1 ≥ 0 and its boundary to contain a segment of the hyperplane {x1 = 0} where non-homogeneous Dirichlet conditions are imposed. We are then looking for the solution of a partial differential equation satisfying a Dirichlet and a Neumann boundary condition simultaneously on the free boundary. The existence and uniqueness of a solution have already been addressed...
On a Brezis-Nirenberg type problem.
On a class of Monge-Ampére problems with non-homogeneous Dirichlet boundary condition.
On a class of Monge-Ampère type equations with lower order terms
We prove some comparison results for Monge-Ampère type equations in dimension two. We consider also the case of eigenfunctions and we prove a kind of reverse inequalities.
On a conjecture relative to the maximum of harmonic functions on convex domains: Unbounded domains.
On a hierarchical basis multilevel method with nonconforming P1 elements.
On a inequality of Friedrichs.
On a parallel implementation of the mortar element method
On a Parallel Implementation of the Mortar Element Method
We discuss a parallel implementation of the domain decomposition method based on the macro-hybrid formulation of a second order elliptic equation and on an approximation by the mortar element method. The discretization leads to an algebraic saddle- point problem. An iterative method with a block- diagonal preconditioner is used for solving the saddle- point problem. A parallel implementation of the method is emphasized. Finally the results of numerical experiments are presented.
On a perturbed Dirichlet problem for a nonlocal differential equation of Kirchhoff type.
On a potential problem with incident wave as a field source
On a semilinear elliptic eigenvalue problem
We obtain a description of the spectrum and estimates for generalized positive solutions of -Δu = λ(f(x) + h(u)) in Ω, , where f(x) and h(u) satisfy minimal regularity assumptions.
On a sub-supersolution method for the prescribed mean curvature problem
The paper is about a sub-supersolution method for the prescribed mean curvature problem. We formulate the problem as a variational inequality and propose appropriate concepts of sub- and supersolutions for such inequality. Existence and enclosure results for solutions and extremal solutions between sub- and supersolutions are established.
On a superconvergent finite element scheme for elliptic systems. I. Dirichlet boundary condition
Second order elliptic systems with Dirichlet boundary conditions are solved by means of affine finite elements on regular uniform triangulations. A simple averagign scheme is proposed, which implies a superconvergence of the gradient. For domains with enough smooth boundary, a global estimate is proved in the -norm. For a class of polygonal domains the global estimate can be proven.
On a superconvergent finite element scheme for elliptic systems. II. Boundary conditions of Newton's or Neumann's type
A simple superconvergent scheme for the derivatives of finite element solution is presented, when linear triangular elements are employed to solve second order elliptic systems with boundary conditions of Newton’s or Neumann’s type. For bounded plane domains with smooth boundary the local -superconvergence of the derivatives in the -norm is proved. The paper is a direct continuations of [2], where an analogous problem with Dirichlet’s boundary conditions is treated.