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Regularity results for minimizers of non-autonomous integral functionals
Antonio Giuseppe Grimaldi, Stefania Russo
We establish the higher fractional differentiability for the minimizers of non-autonomous integral functionals of the form \begin{equation} \mathcal{F}(u,Ω):=\int_Ω\left[ f(x,Du)-…
Gradient regularity for a class of elliptic obstacle problems
Raffaella Giova, Antonio Giuseppe Grimaldi, Andrea Torricelli
We prove some regularity results for a priori bounded local minimizers of non-autonomous integral functionals of the form under the constraint…
Regularity for minimizers of scalar integral functionals
Antonio Giuseppe Grimaldi, Elvira Mascolo, Antonia Passarelli di Napoli
We prove the local Lipschitz regularity of the local minimizers of scalar integral functionals of the form \begin{equation*} \mathcal{F}(v;Ω)= \int_Ω f (x, Dv) dx \end{equation*} u…
Regularity results for Hölder minimizers to functionals with non-standard growth
Antonio Giuseppe Grimaldi, Erica Ipocoana
We study the regularity properties of Hölder continuous minimizers to non-autonomous functionals satisfying -growth conditions, under Besov assumptions on the coefficients.…
On the second-order regularity of solutions to widely singular or degenerate elliptic equations
Pasquale Ambrosio, Antonio Giuseppe Grimaldi, Antonia Passarelli di Napoli
We consider local weak solutions to PDEs of the type \[ -\,\mathrm{div}\left((\vert Du\vert-λ)_{+}^{p-1}\frac{Du}{\vert Du\vert}\right)=f\,\,\,\,\,\,\,\text{in}\,\,Ω, \] where $1<p…