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of 35
pro vyhledávání: '"D'Ambrosio, Pasquale"'
Autor:
Ambrosio, Pasquale
Publikováno v:
Calc. Var. 64, 32 (2025)
We consider local weak solutions to the widely degenerate parabolic PDE \[ \partial_{t}u-\mathrm{div}\left((\vert Du\vert-\lambda)_{+}^{p-1}\frac{Du}{\vert Du\vert}\right)=f\,\,\,\,\,\,\,\,\mathrm{in}\,\,\,\Omega_{T}=\Omega\times(0,T), \] where $p\ge
Externí odkaz:
http://arxiv.org/abs/2407.05432
We consider local weak solutions of widely degenerate or singular elliptic PDEs of the type \begin{equation*} -\,\mathrm{div}\left((\vert Du\vert-\lambda)_{+}^{p-1}\frac{Du}{\vert Du\vert}\right)=f \,\,\,\,\,\,\, \text{in}\,\,\Omega, \end{equation*}
Externí odkaz:
http://arxiv.org/abs/2401.13116
Autor:
Ambrosio, Pasquale, Bäuerlein, Fabian
Publikováno v:
Journal of Differential Equations (2024)
We consider weak solutions $u:\Omega_{T}\rightarrow\mathbb{R}^{N}$ to parabolic systems of the type \[ u_{t}-\mathrm{div}\,A(x,t,Du)=f \qquad \mathrm{in}\ \Omega_{T}=\Omega\times(0,T), \] where $\Omega$ is a bounded open subset of $\mathbb{R}^{n}$ fo
Externí odkaz:
http://arxiv.org/abs/2312.13760
Publikováno v:
Engineering with Computers (2024)
In recent years, Scientific Machine Learning (SciML) methods for solving partial differential equations (PDEs) have gained increasing popularity. Within such a paradigm, Physics-Informed Neural Networks (PINNs) are novel deep learning frameworks for
Externí odkaz:
http://arxiv.org/abs/2310.00172
Autor:
Ambrosio, Pasquale
Publikováno v:
Forum Mathematicum. 2023
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)_{+}^{p-1}\frac{Du}{\vert Du\vert}\right]=f\,\,\,\,\,\,\,\,\,\mathrm{in}\,\,
Externí odkaz:
http://arxiv.org/abs/2210.02581
Publikováno v:
Advances in Calculus of Variations. 2023
Motivated by applications to gas filtration problems, we study the regularity of weak solutions to the strongly degenerate parabolic PDE $u_{t}-\mathrm{div}\left((\vert Du\vert-\nu)_{+}^{p-1}\frac{Du}{\vert Du\vert}\right)=f$ in $\Omega_{T}=\Omega\ti
Externí odkaz:
http://arxiv.org/abs/2204.05966
Autor:
Ambrosio, Pasquale, Bäuerlein, Fabian
Publikováno v:
In Journal of Differential Equations 25 August 2024 401:492-549
Autor:
Ambrosio, Pasquale
Publikováno v:
J. Math. Anal.Appl.(2021), 12563
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 elliptic PDE $-\mathrm{div}\left((\vert\nabla u\vert-1)_{+}^{q-1}\frac{
Externí odkaz:
http://arxiv.org/abs/2104.02795
Autor:
Ambrosio, Pasquale
Publikováno v:
In Journal of Mathematical Analysis and Applications 15 January 2022 505(2)
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