Maximal solutions of equation u = uq in arbitrary domains

Original · EN

We prove bilateral capacitary estimates for the maximal solution UF of -Δu+uq=0 in the complement of an arbitrary closed set Fⁿ, involving the Bessel capacity C₂,q', for q in the supercritical range q≥ qc:=N/(N-2). We derive a pointwise necessary and sufficient condition, via a Wiener type criterion, in order that UF(x)→∞ as x→ y for given y∈ F. Finally we prove a general uniqueness result for large solutions.