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- W2891874328 abstract "We study integral operators $mathcal{L}u(x)=int_{mathbb{R^N}}psi(u(x)-u(y))J(x-y),dy$ of the type of the fractional $p$-Laplacian operator, and the properties of the corresponding Orlicz and Sobolev-Orlicz spaces. In particular we show a Poincare inequality and a Sobolev inequality, depending on the singularity at the origin of the kernel $J$ considered, which may be very weak. Both inequalities lead to compact inclusions. We then use those properties to study the associated elliptic problem $mathcal{L}u=f$ in a bounded domain $Omega$, and boundary condition $uequiv0$ on $Omega^c$; both cases $f=f(x)$ and $f=f(u)$ are considred, including the generalized eigenvalue problem $f(u)=lambdapsi(u)$." @default.
- W2891874328 created "2018-09-27" @default.
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- W2891874328 date "2018-09-04" @default.
- W2891874328 modified "2023-09-27" @default.
- W2891874328 title "Remarks on a nonlinear nonlocal operator in Orlicz spaces" @default.
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