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On the continuity of degenerate n-harmonic functions

Flavia Giannetti, Antonia Passarelli di Napoli (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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 = . ∫ 1 ∞ P ( t ) t 2   d t = ∞ .

On the continuity of degenerate n-harmonic functions

Flavia Giannetti, Antonia Passarelli di Napoli (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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 critical Neumann problem with lower order perturbations

Jan Chabrowski, Bernhard Ruf (2007)

Colloquium Mathematicae

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.

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