On the regularity of the free boundary for quasilinear obstacle problems

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dc.contributor.authorChallal, Samia
dc.contributor.authorLyaghfouri, Abdeslem
dc.contributor.authorRodrigues, José Francisco
dc.contributor.authorTeymurazyan, Rafayel
dc.date.accessioned2025-03-10T22:02:05Z
dc.date.available2025-03-10T22:02:05Z
dc.date.issued2014-09-19
dc.description.abstractWe extend basic regularity of the free boundary of the obstacle problem to some classes of heterogeneous quasilinear elliptic operators with variable growth that includes, in particular, the p(x)-Laplacian. Under the assumption of Lipschitz continuity of the order of the power growth p(x) > 1, we use the growth rate of the solution near the free boundary to obtain its porosity, which implies that the free boundary is of Lebesgue measure zero for p(x)-Laplacian type heterogeneous obstacle problems. Under additional assumptions on the operator heterogeneities and on data we show, in two different cases, that up to a negligible singular set of null perimeter the free boundary is the union of at most a countable family of C1 hypersurfaces: (i) by extending directly the finiteness of the (n - 1)-dimensional Hausdorff measure of the free boundary to the case of heterogeneous p-Laplacian type operators with constant p, 1 < p < ∞; (ii) by proving the characteristic function of the coincidence set is of bounded variation in the case of non degenerate or non singular operators with variable power growth p(x) > 1.
dc.description.sponsorshipThe first and second authors are grateful for the excellent research facilities at the Fields Institute during their visits at this institute.
dc.identifier.citationSamia Challal, Abdeslem Lyaghfouri, José Francisco Rodrigues, Rafayel Teymurazyan, On the regularity of the free boundary for quasilinear obstacle problems. Interfaces Free Bound. 16 (2014), no. 3, pp. 359–394. DOI 10.4171/IFB/323
dc.identifier.issn1463-9963
dc.identifier.issn1463-9971
dc.identifier.urihttps://doi.org/10.4171/ifb/323
dc.identifier.urihttps://hdl.handle.net/10315/42665
dc.language.isoen
dc.publisherEuropean Mathematical Society - EMS - Publishing House
dc.rightsAttribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectApplied mathematics
dc.subjectMathematical physics
dc.subjectPure mathematics
dc.subjectMathematical sciences
dc.subjectObstacle problem
dc.subjectRegularity of the free boundary
dc.subjectQuasi-linear elliptic operators
dc.subjectHeterogeneous p-Laplacian
dc.symplectic.issue3
dc.symplectic.journalInterfaces and Free Boundaries Mathematical Analysis Computation and Applications
dc.symplectic.pagination359-394
dc.symplectic.subtypeJournal article
dc.symplectic.volume16
dc.titleOn the regularity of the free boundary for quasilinear obstacle problems
dc.typeArticle

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