On the continuation of solutions for elliptic equations in two variables
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 = ∞ .
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
We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent and lower order perturbations in bounded domains. Solutions are obtained by min max methods based on a topological linking. A nonlinear perturbation of a lower order is allowed to interfere with the spectrum of the operator -Δ with the Neumann boundary conditions.