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Descrizione Pasquale Ambrosio (University of Naples “Federico II”) “Regularity results for a class of strongly degenerateparabolic equations” Motivated by applications to gas filtration problems, we study the regularity of weak solutions to the strongly
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Descrizione
Pasquale Ambrosio (University of Naples “Federico II”)
“Regularity results for a class of strongly degenerateparabolic equations”
Motivated by applications to gas filtration problems, we study the
regularity of weak solutions to the strongly degenerateparabolic PDE
ut – div [((|Du| – 𝜈)+)^{p-1}Du/|Du|] = f in ΩT = Ω × (0, T),
where Ω is a bounded domain in Rn for n ≥ 2, p ≥ 2, 𝜈 is a positive
constant and (⋅)+ stands for the positive part. Assumingthat the datum
f belongs to a suitable Lebesgue-Sobolev parabolic space, weestablish
the Sobolev spatial regularity of a nonlinear function ofthe spatial
gradient Du of the weak solutions, which in turn implies theexistence
of the weak time derivative ut. Next, we weaken theassumption on the
right-hand side, by assuming that f belongs to a suitablelocal
Lebesgue-Besov space. This leads us to obtain fractionalSobolev
regularity results for a function of Du, which in turn yieldthe higher
summability of Du with respect to the spatial variable. Themain novelty
here is that the structure function of the above equationsatisfies
standard growth and ellipticity conditions only outside theball with
radius 𝜈 centered at the origin.
This is a joint research with Antonia Passarelli di Napoli(University
of Naples “Federico II”).
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Emanuele Cristoforoni (SSM)
Titolo: A thermal insulation problem witha prescribed heat source
Abstract: We study the thermal insulationof a bounded body $Omegasubsetmathbb{R}^n$, 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.
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(Mercoledì) 15:00 - 16:30