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Remarks on a nonlinear nonlocal operator in Orlicz spaces

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URI: https://hdl.handle.net/10016/38908
ISSN: 2191-9496
DOI: https://doi.org/10.1515/anona-2020-0002
UXXI: AR/0000022067
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remarks_ANA_2018.pdf (319.66 KB)
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2019-05-22
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De Gruyter
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We study integral operators Lu(x)=∫RNpsi(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 Poincaré 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 Lu=f in a bounded domain Omega, and boundary condition u≡0 on Omegac; both cases f=f(x) and f=f(u) are considred, including the generalized eigenvalue problem f(u)=lambdapsi(u).
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Nonlocal equations, Integral operators, p–fractional laplacian, Orlicz spaces
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Correa, E., & Pablo, A. de. (2019). Remarks on a nonlinear nonlocal operator in Orlicz spaces. Advances in Nonlinear Analysis, 9(1) pp. 305-326.
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