On the behaviour of the solutions to p-Laplacian equations as p goes to 1
On the continuity of degenerate n-harmonic functions
We study the regularity of finite energy solutions to degenerate n-harmonic equations. The function K(x), which measures the degeneracy, is assumed to be subexponentially integrable, i.e. it verifies the condition exp(P(K)) ∈ Lloc1. The function P(t) is increasing on [0,∞[ and satisfies the divergence condition∫ 1 ∞ P ( t ) t 2 d t = ∞ .
On the continuity of degenerate n-harmonic functions
We study the regularity of finite energy solutions to degenerate n-harmonic equations. The function K(x), which measures the degeneracy, is assumed to be subexponentially integrable, i.e. it verifies the condition exp(P(K)) ∈ Lloc1. The function P(t) is increasing on [0,∞[ and satisfies the divergence condition
On the convergence of Laplace-Beltrami operators associated to quasiregular mappings
On the dimension of -harmonic measure in space
Let , and let , be given. In this paper we study the dimension of -harmonic measures that arise from non-negative solutions to the -Laplace equation, vanishing on a portion of , in the setting of -Reifenberg flat domains. We prove, for , that there exists small such that if is a -Reifenberg flat domain with , then -harmonic measure is concentrated on a set of -finite -measure. We prove, for , that for sufficiently flat Wolff snowflakes the Hausdorff dimension of -harmonic measure...
On the Dirichlet problem for a degenerate elliptic equation
On the Dirichlet problem for a second order elliptic system with degeneration on the entire domain boundary.
On the Dirichlet problem for nonlinear degenerate elliptic equations and applications to optimal control.
On the Dirichlet problem for quasilinear elliptic second order equations with triple degeneracy and singularity in a domain with a boundary conical point.
On the eigenvalue problem for the Hardy-Sobolev operator with indefinite weights.
On the existence of positive solutions of Yamabe-type equations on the Heisenberg group.
On the existence of weak solutions for -Laplacian systems with weights.
On the fusion problem for degenerate elliptic equations II
Let be a relatively closed subset of a Euclidean domain . We investigate when solutions to certain elliptic equations on are restrictions of solutions on all of . Specifically, we show that if is not too large, and has a suitable decay rate near , then can be so extended.
On the interior regularity of weak solutions of degenerate elliptic systems (the case < < )
On the penalized obstacle problem in the unit half ball.
On the properties of infinity-harmonic functions and an application to capacitary convex rings.
On the quasiuniqueness of solutions of degenerate equations in Hilbert space.
On the radial solutions of a degenerate quasilinear elliptic equation in
On the sets of regularity of solutions for a class of degenerate nonlinear elliptic fourth-order equations with data.
On the solution of the Dirichlet problem for an elliptic equation degenerating on the boundary.