Elliptic equations involving the 1-Laplacian and a total variation term with L^{N,\infty}-data
dc.contributor.author | Latorre, Marta | |
dc.contributor.author | Segura de León, Sergio | |
dc.date.accessioned | 2024-04-03T06:18:05Z | |
dc.date.available | 2024-04-03T06:18:05Z | |
dc.date.issued | 2017 | |
dc.identifier.citation | Marta Latorre, Sergio Segura de León, Elliptic equations involving the 1-Laplacian and a total variation term with L^{N,\infty}-data. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 28 (2017), no. 4, pp. 817–859 | es |
dc.identifier.issn | 1120-6330 | |
dc.identifier.uri | https://hdl.handle.net/10115/31912 | |
dc.description.abstract | In this paper we study, in an open bounded set with Lipschitz boundary, the Dirichlet problem for a nonlinear singular elliptic equation involving the 1--Laplacian and a total variation term, that is, the inhomogeneous case of the equation appearing in the level set formulation of the inverse mean curvature flow. Our aim is twofold. On the one hand, we consider data belonging to the Marcinkiewicz space with a critical exponent, which leads to unbounded solutions. So, we have to begin introducing the suitable notion of unbounded solution to this problem. Moreover, examples of explicit solutions are shown. On the other hand, this equation allows us to deal with many related problems having a different gradient term which depend on a function g. It is known that the total variation term induces a regularizing effect on existence, uniqueness and regularity. We focus on analyzing whether those features remain true when general gradient terms are taken. Roughly speaking, the bigger g, the better the properties of the solution. | es |
dc.language.iso | eng | es |
dc.subject | 1-Laplacian | es |
dc.subject | total variation | es |
dc.subject | unbounded solutions | es |
dc.subject | inverse mean curvature flow | es |
dc.title | Elliptic equations involving the 1-Laplacian and a total variation term with L^{N,\infty}-data | es |
dc.type | info:eu-repo/semantics/article | es |
dc.identifier.doi | 10.4171/RLM/787 | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
Files in this item
This item appears in the following Collection(s)
-
Artículos de Revista [4166]
Los ítems de digital-BURJC están protegidos por copyright, con todos los derechos reservados, a menos que se indique lo contrario