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Davide Guidetti

Publications and source records attributed to Davide Guidetti.

6 recordsLinked to original sources
arXiv2018

On maximal regularity for the Cauchy-Dirichlet mixed parabolic problem with fractional time derivative

We prove two maximal regularity results in spaces of continuous and Hölder continuous functions, for a mixed linear Cauchy-Dirichlet problem with a fractional time derivative $\mathbb{D}_t^α$. This derivative is intended in the sense of Caputo and $α$ is taken in $(0, 2)$. In case $α= 1$, we obtain maximal regularity results for mixed parabolic problems already known in mathematica literature.

math.AP↗
arXiv2014

$\mathsf{L}^1$-elliptic regularity and $H=W$ on the whole $\mathsf{L}^p$-scale on arbitrary manifolds

We define abstract Sobolev type spaces on $\mathsf{L}^p$-scales, $p\in [1,\infty)$, on Hermitian vector bundles over possibly noncompact manifolds, which are induced by smooth measures and families $\mathfrak{P}$ of linear partial differential operators, and we prove the density of the corresponding smooth Sobolev sections in these spaces under a generalized ellipticity condition on the underlying family. In particular, this implies a covariant version of Meyers-Serrin\rq{}s theorem on the whole $\mathsf{L}^p$-scale, for arbitrary Riemannian manifolds. Furthermore, we prove a new local elliptic regularity result in $\mathsf{L}^1$ on the Besov scale, which shows that the above generalized ellipticity condition is satisfied on the whole $\mathsf{L}^p$-scale, if some differential operator from $\mathfrak{P}$ that has a sufficiently high (but not necessarily the highest) order is elliptic.

math.AP↗
arXiv2013

Identification of a convolution kernel in a control problem for the heat equation with a boundary memory term

We consider the evolution of the temperature $u$ in a material with thermal memory characterized by a time-dependent convolution kernel $h$. The material occupies a bounded region $Ω$ with a feedback device controlling the external temperature located on the boundary $Γ$. Assuming both $u$ and $h$ unknown, we formulate an inverse control problem for an integrodifferential equation with a nonlinear and nonlocal boundary condition. Existence and uniqueness results of a solution to the inverse problem are proved.

math.AP↗