Descrizione<\/p>\n
Pasquale Ambrosio (University of Naples \u201cFederico II\u201d)<\/p>\n
“Regularity results for a class of strongly degenerateparabolic equations”<\/p>\n
Motivated by applications to gas filtration problems, we study the<\/p>\n
regularity of weak solutions to the strongly degenerateparabolic PDE<\/p>\n
ut – div [((|Du| – \ud835\udf08)+)^{p-1}Du\/|Du|] = f in \u03a9T = \u03a9 \u00d7 (0, T),<\/p>\n
where \u03a9 is a bounded domain in Rn for n \u2265 2, p \u2265 2, \ud835\udf08 is a positive<\/p>\n
constant and (\u22c5)+ stands for the positive part. Assumingthat the datum<\/p>\n
f belongs to a suitable Lebesgue-Sobolev parabolic space, weestablish<\/p>\n
the Sobolev spatial regularity of a nonlinear function ofthe spatial<\/p>\n
gradient Du of the weak solutions, which in turn implies theexistence<\/p>\n
of the weak time derivative ut. Next, we weaken theassumption on the<\/p>\n
right-hand side, by assuming that f belongs to a suitablelocal<\/p>\n
Lebesgue-Besov space. This leads us to obtain fractionalSobolev<\/p>\n
regularity results for a function of Du, which in turn yieldthe higher<\/p>\n
summability of Du with respect to the spatial variable. Themain novelty<\/p>\n
here is that the structure function of the above equationsatisfies<\/p>\n
standard growth and ellipticity conditions only outside theball with<\/p>\n
radius \ud835\udf08 centered at the origin.<\/p>\n
This is a joint research with Antonia Passarelli di Napoli(University<\/p>\n
of Naples \u201cFederico II\u201d).<\/p>\n
————————————————————————————————————-<\/p>\n
Emanuele Cristoforoni (SSM)<\/p>\n
Titolo: A thermal insulation problem witha prescribed heat source<\/p>\n
Abstract: We study the thermal insulationof a bounded body $\\Omega\\subset\\mathbb{R}^n$, under a prescribed heat source$f > 0$, via a bulk layer of insulating material. We consider a model ofheat transfer between the insulated body and the environment determined byconvection; this corresponds to Robin boundary conditions on the free boundaryof the layer. We show that a minimal con guration exists and that it satisfiesuniform density estimates.<\/p>\n","protected":false},"author":1,"featured_media":-1,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"tags":[],"event_type":[],"event_type_2":[],"class_list":["post-1772","ajde_events","type-ajde_events","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=\/wp\/v2\/ajde_events\/1772","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=\/wp\/v2\/ajde_events"}],"about":[{"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=\/wp\/v2\/types\/ajde_events"}],"author":[{"embeddable":true,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1772"}],"version-history":[{"count":0,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=\/wp\/v2\/ajde_events\/1772\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1772"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1772"},{"taxonomy":"event_type","embeddable":true,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=%2Fwp%2Fv2%2Fevent_type&post=1772"},{"taxonomy":"event_type_2","embeddable":true,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=%2Fwp%2Fv2%2Fevent_type_2&post=1772"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}