{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T15:48:18Z","timestamp":1776440898245,"version":"3.51.2"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Interfaces Free Bound."],"published-print":{"date-parts":[[2014,9,19]]},"abstract":"<jats:p>\n                    We 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\n                    <jats:inline-formula>\n                      <jats:tex-math>p(x)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    -Laplacian. Under the assumption of Lipschitz continuity of the order of the power growth\n                    <jats:inline-formula>\n                      <jats:tex-math>p(x)&gt;1<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , 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\n                    <jats:inline-formula>\n                      <jats:tex-math>p(x)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    -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\n                    <jats:inline-formula>\n                      <jats:tex-math>C^1<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    hypersurfaces: i) by extending directly the finiteness of the\n                    <jats:inline-formula>\n                      <jats:tex-math>(n-1)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    -dimensional Hausdorff measure of the free boundary to the case of heterogeneous\n                    <jats:inline-formula>\n                      <jats:tex-math>p<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    -Laplacian type operators with constant\n                    <jats:inline-formula>\n                      <jats:tex-math>p, 1 &lt; p &lt;\\infty<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ; 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\n                    <jats:inline-formula>\n                      <jats:tex-math>p(x)&gt;1<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    .\n                  <\/jats:p>","DOI":"10.4171\/ifb\/323","type":"journal-article","created":{"date-parts":[[2014,9,19]],"date-time":"2014-09-19T17:45:05Z","timestamp":1411148705000},"page":"359-394","source":"Crossref","is-referenced-by-count":11,"title":["On the regularity of the free boundary for quasilinear obstacle problems"],"prefix":"10.4171","volume":"16","author":[{"given":"Samia","family":"Challal","sequence":"first","affiliation":[{"name":"York University, Toronto, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0957-9675","authenticated-orcid":false,"given":"Abdeslem","family":"Lyaghfouri","sequence":"additional","affiliation":[{"name":"The Fields Institute for Research in Mathematical Sciences, Toronto, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8438-0749","authenticated-orcid":false,"given":"Jos\u00e9 Francisco","family":"Rodrigues","sequence":"additional","affiliation":[{"name":"FC Universidade de Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5263-8992","authenticated-orcid":false,"given":"Rafayel","family":"Teymurazyan","sequence":"additional","affiliation":[{"name":"Universidade de Lisboa, Portugal"}]}],"member":"2673","container-title":["Interfaces and Free Boundaries, Mathematical Analysis, Computation and Applications"],"original-title":[],"link":[{"URL":"http:\/\/www.ems-ph.org\/fulltext\/10.4171\/IFB\/323","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T12:51:53Z","timestamp":1762951913000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/ifb\/323"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,9,19]]},"references-count":0,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.4171\/ifb\/323","relation":{},"ISSN":["1463-9963","1463-9971"],"issn-type":[{"value":"1463-9963","type":"print"},{"value":"1463-9971","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,9,19]]}}}