Estimates for the first eigenfunction of linear eigenvalue problems via Steiner symmetrization.
Estimates for the multiplicative square function of solutions to nondivergence elliptic equations.
Estimates from above and from below for the Homogenized Coefficients.
Estimates of eigenvalues and eigenfunctions in periodic homogenization
For a family of elliptic operators with rapidly oscillating periodic coefficients, we study the convergence rates for Dirichlet eigenvalues and bounds of the normal derivatives of Dirichlet eigenfunctions. The results rely on an estimate in for solutions with Dirichlet condition.
Estimates of solutions to linear elliptic systems and equations
Whenever nonlinear problems have to be solved through approximation methods by solving related linear problems a priori estimates are very useful. In the following this kind of estimates are presented for a variety of equations related to generalized first order Beltrami systems in the plane and for second order elliptic equations in . Different types of boundary value problems are considered. For Beltrami systems these are the Riemann-Hilbert, the Riemann and the Poincaré problem, while for elliptic...
Estimates of the principal eigenvalue of the -Laplacian and the -biharmonic operator
We survey recent results concerning estimates of the principal eigenvalue of the Dirichlet -Laplacian and the Navier -biharmonic operator on a ball of radius in and its asymptotics for approaching and . Let tend to . There is a critical radius of the ball such that the principal eigenvalue goes to for and to for . The critical radius is for any for the -Laplacian and in the case of the -biharmonic operator. When approaches , the principal eigenvalue of the Dirichlet...
Estimates on the solution of an elliptic equation related to Brownian motion with drift (II).
In this paper we continue the study of the Dirichlet problem for an elliptic equation on a domain in R3 which was begun in [5]. For R > 0 let ΩR be the ball of radius R centered at the origin with boundary ∂Ω R. The Dirichlet problem we are concerned with is the following:(-Δ - b(x).∇) u(x) = f(x), x ∈ Ω R,with zero boundary conditionsu(x) = 0, x ∈ ∂Ω R.
Estimates on the solution of an elliptic equation related to Brownian motion with drift.
In this paper we are concerned with studying the Dirichlet problem for an elliptic equation on a domain in R3. For simplicity we shall assume that the domain is a ball ΩR of radius R. Thus:ΩR = {x ∈ R3 : |x| < R}.The equation we are concerned with is given by(-Δ - b(x).∇) u(x) = f(x), x ∈ ΩR,with zero Dirichlet boundary conditions.
Étude du nombre de solutions pour une classe d'équations elliptiques non-linéaires qui se prolongent en problèmes à frontière libre
Evaluation of the condition number in linear systems arising in finite element approximations
This paper derives upper and lower bounds for the -condition number of the stiffness matrix resulting from the finite element approximation of a linear, abstract model problem. Sharp estimates in terms of the meshsize h are obtained. The theoretical results are applied to finite element approximations of elliptic PDE's in variational and in mixed form, and to first-order PDE's approximated using the Galerkin–Least Squares technique or by means of a non-standard Galerkin technique in L1(Ω). Numerical...
Exact solutions to some external mixed problems in potential theory
A new and elegant procedure is proposed for the solution of mixed potential problems in a half-space with a circular line of division of boundary conditions. The approach is based on a new type of integral operators with special properties. Two general external problems are solved; i) An arbitrary potential is specified at the boundary outside a circle, and its normal derivative is zero inside; ii) An arbitrary normal derivative is given outside the circle, and be potential is zero inside. Several...
Existence and concentration of solutions for a -Laplace equation with potentials in .
Existence and location of solution to some eigenvalue Dirichlet problems.
Existence and multiplicity of nontrivial solutions for double resonance semilinear elliptic problems.
Existence and multiplicity of solutions for the noncoercive Neumann -Laplacian.
Existence and multiplicity of solutions to elliptic problems with discontinuities and free boundary conditions.
Existence and multiplicity results for a semilinear elliptic eigenvalue problem
Existence and multiplicity results for degenerate elliptic equations with dependence on the gradient.
Existence and multiplicity results for nonlinear elliptic problems in with an indefinite functional.
Existence and nonexistence of classical solutions of the Dirichlet problem for a class of fully nonlinear nonuniformly elliptic equations