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dc.contributor.author
Casari Rampasso, Giane
dc.contributor.author
Wolanski, Noemi Irene
dc.date.available
2022-08-31T19:08:29Z
dc.date.issued
2021-03-04
dc.identifier.citation
Casari Rampasso, Giane; Wolanski, Noemi Irene; A minimization problem for the p(x)-Laplacian involving area; Springer Heidelberg; Annali Di Matematica Pura Ed Applicata; 200; 5; 4-3-2021; 2155-2179
dc.identifier.issn
0373-3114
dc.identifier.uri
http://hdl.handle.net/11336/167081
dc.description.abstract
In the present article we study a minimization problem in RN involving the perimeter of the positivity set of the solution u and the integral of | ∇ u| p(x). Here p(x) is a Lipschitz continuous function such that 1 < pmin≤ p(x) ≤ pmax< ∞. We prove that such a minimizing function exists and that it is a classical solution to a free boundary problem. In particular, the reduced free boundary is a C2 surface and the dimension of the singular set is at most N- 8. Under further regularity assumptions on the exponent p(x) we get more regularity of the free boundary. In particular, if p∈ C∞ we have that ∂red{ u> 0 } is a C∞ surface.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer Heidelberg
dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by/2.5/ar/
dc.subject
FREE BOUNDARY PROBLEMS
dc.subject
MEAN CURVATURE
dc.subject
VARIABLE EXPONENT SPACES
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
A minimization problem for the p(x)-Laplacian involving area
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2022-08-23T20:46:43Z
dc.identifier.eissn
1618-1891
dc.journal.volume
200
dc.journal.number
5
dc.journal.pagination
2155-2179
dc.journal.pais
Alemania
dc.journal.ciudad
Heidelberg
dc.description.fil
Fil: Casari Rampasso, Giane. Universidade Estadual de Campinas; Brasil
dc.description.fil
Fil: Wolanski, Noemi Irene. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
dc.journal.title
Annali Di Matematica Pura Ed Applicata
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.1007/s10231-021-01073-x
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s10231-021-01073-x
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