Given p> 1 and f Lipschitz, under appropriate assumptions on the smoothness of the bounded domain Ω⊂RN,N≥1, we give a precise description of the asymptotic behaviour of the gradient of the unique solution of {-Δu+|u|p-1u=finΩ,u=+∞on∂Ω.In particular, we show that there exists a corrector function S, finite sum of singular terms, such that z:=u-S∈W1,∞(Ω).Moreover, we prove that ∀x¯∈∂Ωz(x¯)=0andlimδ→0z(x¯-δν(x¯))δ=0,where ν is the outward unit normal to ∂Ω.
Gradient behaviour for large solutions to semilinear elliptic problems / Buccheri, S.. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 198:3(2019), pp. 1013-1040. [10.1007/s10231-018-0808-y]
Gradient behaviour for large solutions to semilinear elliptic problems
Buccheri S.
2019
Abstract
Given p> 1 and f Lipschitz, under appropriate assumptions on the smoothness of the bounded domain Ω⊂RN,N≥1, we give a precise description of the asymptotic behaviour of the gradient of the unique solution of {-Δu+|u|p-1u=finΩ,u=+∞on∂Ω.In particular, we show that there exists a corrector function S, finite sum of singular terms, such that z:=u-S∈W1,∞(Ω).Moreover, we prove that ∀x¯∈∂Ωz(x¯)=0andlimδ→0z(x¯-δν(x¯))δ=0,where ν is the outward unit normal to ∂Ω.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
