caa a22 4500 606210059 CHVBK 20210128101031.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s00032-015-0235-0 doi (NATIONALLICENCE)springer-10.1007/s00032-015-0235-0 W 1,1(Ω) Solutions of Nonlinear Problems with Nonhomogeneous Neumann Boundary Conditions [Elektronische Daten] [Lucio Boccardo, Lourdes Moreno-Mérida] In this paper we study the existence of W 1,1(Ω) distributional solutions of the nonlinear problems with Neumann boundary condition. The simplest model is $$\left \{ \begin{array}{cc} -\Delta_{p}u + |u|^{s-1}u = 0, & {\rm in}\, \Omega;\\ |\nabla u|^{p-2}\nabla u . \eta = \psi, & {\rm on} \, \partial\Omega;\end{array}\right.$$ - Δ p u + | u | s - 1 u = 0 , in Ω ; | ∇ u | p - 2 ∇ u . η = ψ , on ∂ Ω ; where Ω is a bounded domain in $${I\!R^{N}}$$ I R N with smooth boundary $${\partial\Omega, 1 < p < N, s > 0, \eta}$$ ∂ Ω , 1 < p < N , s > 0 , η is the unit outward normal on $${\partial\Omega {\rm and} \psi \in L^{m}(\partial\Omega), m > 1}$$ ∂ Ω and ψ ∈ L m ( ∂ Ω ) , m > 1 . Springer Basel, 2015 Nonlinear problems nationallicence Neumann boundary condition nationallicence distributional solutions nationallicence Boccardo Lucio Dipartimento di Matematica, "Sapienza” Università di Roma, P.le A. Moro 5, 00185, Roma, Italy aut Moreno-Mérida Lourdes Departamento de Análisis Matematico, Universidad de Granada, Av. Fuentenueva S/N, 18071, Granada, Spain aut Milan Journal of Mathematics Springer Basel 83/2(2015-12-01), 279-293 1424-9286 83:2<279 2015 83 32 https://doi.org/10.1007/s00032-015-0235-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00032-015-0235-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Boccardo Lucio Dipartimento di Matematica, "Sapienza” Università di Roma, P.le A. Moro 5, 00185, Roma, Italy aut NATIONALLICENCE 700 1- Moreno-Mérida Lourdes Departamento de Análisis Matematico, Universidad de Granada, Av. Fuentenueva S/N, 18071, Granada, Spain aut NATIONALLICENCE 773 0- Milan Journal of Mathematics Springer Basel 83/2(2015-12-01), 279-293 1424-9286 83:2<279 2015 83 32