Neumann problems for nonlinear elliptic equations with L-1 data

作者：Betta M F; Guibe O; Mercaldo A^*

来源：Journal of Differential Equations, 2015, 259(3): 898-924.

DOI：10.1016/j.jde.2015.02.031

• Nonlinear elliptic equations
• Neumann problems
• Renormalized solutions
• Existence results

In the present paper we prove existence results for solutions to nonlinear elliptic Neumann problems whose prototype is
{-Delta(p)u - div(c(x)) vertical bar u vertical bar(p-2)u)) = f in Omega,
(vertical bar del u vertical bar(p-2)del u + c(x) vertical bar u vertical bar(p-2)u) . (n) under bar = 0 on partial derivative Omega,
when f is just a summable function. Our approach also allows us to prove a stability result for renormalized solutions and an existence result for operator with a zero order term.

• 出版日期2015-8-5