15 citations · 50 across the 11 of their papers we have counts for
12 papers
Boundedness and contractive estimates for orthotropic, widely degenerate, doubly nonlinear diffusion equations
Pasquale Ambrosio, Matias Vestberg
We study the regularity of weak solutions to doubly nonlinear orthotropic evolution equations of the form \[ \partial_{t}(\vert u\vert^{α-1}u)-\sum_{i=1}^{N}\partial_{i}\left[a_{i}…
Widely degenerate anisotropic diffusion: local boundedness and semicontinuity
Pasquale Ambrosio, Simone Ciani, Giovanni Cupini
We investigate the regularity of local weak solutions to evolution equations of the form \[ \partial_{t}u\,=\,\sum_{i=1}^{n}\,\partial_{x_{i}}\left[a_{i}(x,t)\,(\vert\partial_{x_{i…
Gradient regularity for strongly singular or degenerate elliptic and parabolic equations
Pasquale Ambrosio
We present recent advances in the regularity theory for weak solutions to some classes of elliptic and parabolic equations with strongly singular or degenerate structure. The equat…
Gradient bounds for a widely degenerate orthotropic parabolic equation
Pasquale Ambrosio
In this paper, we consider the following nonlinear parabolic equation \[ \partial_{t}u\,=\,\sum_{i=1}^{n}\partial_{x_{i}}\left[(\vert u_{x_{i}}\vert-δ_{i})_{+}^{p-1}\frac{u_{x_{i}}…
Local boundedness for weak solutions to strongly degenerate orthotropic parabolic equations
Pasquale Ambrosio, Simone Ciani
We prove the local boundedness of local weak solutions to the parabolic equation \[ \partial_{t}u\,=\,\sum_{i=1}^{n}\partial_{x_{i}}\left[(\vert u_{x_{i}}\vert-δ_{i})_{+}^{p-1}\fra…
Regularity of vectorial minimizers for non-uniformly elliptic anisotropic integrals
Pasquale Ambrosio, Giovanni Cupini, Elvira Mascolo
We establish the local boundedness of the local minimizers of non-uniformly elliptic integrals of the form , where is a bounde…
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…
Gradient bounds for strongly singular or degenerate parabolic systems
Pasquale Ambrosio, Fabian Bäuerlein
We consider weak solutions to parabolic systems of the type \[ u_{t}-\mathrm{div}\,A(x,t,Du)=f \qquad \mathrm{in}\ Ω_{T}=Ω\times(0,T), \] where $…
A physics-informed deep learning approach for solving strongly degenerate parabolic problems
Pasquale Ambrosio, Salvatore Cuomo, Mariapia De Rosa
In recent years, Scientific Machine Learning (SciML) methods for solving partial differential equations (PDEs) have gained increasing popularity. Within such a paradigm, Physics-In…
Fractional Sobolev regularity for solutions to a strongly degenerate parabolic equation
Pasquale Ambrosio
We carry on the investigation started in [2] about the regularity of weak solutions to the strongly degenerate parabolic equation \[ u_{t}-\mathrm{div}\left[(\vert Du\vert-1)_{+}^{…
Regularity results for a class of widely degenerate parabolic equations
Pasquale Ambrosio, Antonia Passarelli di Napoli
Motivated by applications to gas filtration problems, we study the regularity of weak solutions to the strongly degenerate parabolic PDE $u_{t}-\mathrm{div}\left((\vert Du\vert-ν)_…
Besov regularity for a class of singular or degenerate elliptic equations
Pasquale Ambrosio
Motivated by applications to congested traffic problems, we establish higher integrability results for the gradient of local weak solutions to the strongly degenerate or singular e…