Elliptic equations with critical growth and a large set of boundary singularities

Elliptic Equations with Critical Growth and a Large Set of Boundary Singularities

We solve variationally certain equations of stellar dynamics of the form − ∑ i ∂iiu(x) = |u|p−2u(x) dist(x,A)s in a domain Ω of R, where A is a proper linear subspace of R. Existence problems are related to the question of attainability of the best constant in the following recent inequality of BadialeTarantello [1]: 0 < μs,P (Ω) = inf {

Hardy-Sobolev Critical Elliptic Equations with Boundary Singularities

Unlike the non-singular case s = 0, or the case when 0 belongs to the interior of a domain Ω in IR(n ≥ 3), we show that the value and the attainability of the best Hardy-Sobolev constant on a smooth domain Ω, μs(Ω) := inf {

Existence of Critical Elliptic Systems with Boundary Singularities

Adaptive Methods for Semi-linear Elliptic Equations with Critical Exponents and Interior Singularities Adaptive Methods for Semi-linear Elliptic Equations with Critical Exponents and Interior Singularities

We consider the eeectiveness of adaptive nite-element methods for nding the nite element solutions of the parametrised semi-linear elliptic equation u+u+u 5 = 0; u > 0, where u 2 C 2 ((); for a domain IR 3 and u = 0 on the boundary of : This equation is important in analysis and it is known that there is a value 0 > 0 such that no solutions exist for < 0 and a singularity forms as ! 0. Furtherm...

Boundary singularities of solutions to elliptic viscous Hamilton-Jacobi equations

Contents 1 Introduction 2 2 The Dirichlet problem and the boundary trace 7 2. Abstract We study the boundary value problem with measures for (E1) −∆u + g(|∇u|) = 0 in a bounded domain Ω in R N , satisfying (E2) u = µ on ∂Ω and prove that if g ∈ L 1 (1, ∞; t −(2N +1)/N dt) is nondecreasing (E1)-(E2) can be solved with any positive bounded measure. When g(r) ≥ r q with q > 1 we prove that any pos...