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dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.eng
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dc.contributor.authorDipierro, Serena
dc.contributor.authorRos-Oton, Xavier
dc.contributor.authorValdinoci, Enrico
dc.description.abstractWe introduce a new Neumann problem for the fractional Laplacian arising from a simple probabilistic consideration, and we discuss the basic properties of this model. We can consider both elliptic and parabolic equations in any domain. In addition,we formulate problems with nonhomogeneous Neumann conditions, and also with mixed Dirichlet and Neumann conditions, all of them having a clear probabilistic interpretation. We prove that solutions to the fractional heat equation with homogeneous Neumann conditions have the following natural properties: conservation of mass, decreasing energy, and convergence to a constant as time flows. Moreover, for the elliptic case we give the variational formulation of the problem, and establish existence of solutions. We also study the limit properties and the boundary behavior induced by this nonlocal Neumann condition.
dc.publisherBerlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
dc.relation.ispartofseriesPreprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 1986, ISSN 2198-5855-
dc.subjectNonlocal operators
dc.subjectfractional Laplacian
dc.subjectNeumann problem
dc.titleNonlocal problems with Neumann boundary conditions
wgl.typeReport / Forschungsbericht / Arbeitspapierger
dcterms.bibliographicCitation.journalTitlePreprint / Weierstraß-Institut für Angewandte Analysis und Stochastik-
Appears in Collections:Mathematik

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