Zobrazeno 1 - 10
of 14
pro vyhledávání: '"Paolo Bonicatto"'
Autor:
Adolfo Arroyo-Rabasa, Paolo Bonicatto
Publikováno v:
Calculus of Variations and Partial Differential Equations. 62
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::af91454545e6eb0f798f4d2b50326910
https://doi.org/10.1007/s00526-022-02350-0
https://doi.org/10.1007/s00526-022-02350-0
Autor:
Paolo Bonicatto
Publikováno v:
The interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity. 9:489-497
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::42cfdfdf376cfae650c3c0df498cb904
https://doi.org/10.5890/dnc.2020.12.001
https://doi.org/10.5890/dnc.2020.12.001
Publikováno v:
journal de mathématiques pures et appliquées
We deal with the vanishing viscosity scheme for the transport/continuity equation $\partial_t u + \text{div }(u\boldsymbol{b} ) = 0$ drifted by a divergence-free vector field $\boldsymbol{b}$. Under general Sobolev assumptions on $\boldsymbol{b}$, we
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c722cfae25bad0331ac97217d55a4f0d
https://edoc.unibas.ch/84984/
https://edoc.unibas.ch/84984/
Autor:
Paolo Bonicatto, Nikolay A. Gusev
We consider the structure of divergence-free vector measures on the plane. We show that such measures can be decomposed into measures induced by closed simple curves. More generally, we show that if the divergence of a planar vector-valued measure is
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::144361416b6e6be8895c8062e92cd60c
http://wrap.warwick.ac.uk/144969/1/WRAP-On-structure-divergence-free-measures-R2-Bonicatto-2020.pdf
http://wrap.warwick.ac.uk/144969/1/WRAP-On-structure-divergence-free-measures-R2-Bonicatto-2020.pdf
Autor:
Paolo Bonicatto, Elio Marconi
Publikováno v:
Communications in Partial Differential Equations
We consider the regular Lagrangian flow X associated to a bounded divergence-free vector field b with bounded variation. We prove a Lusin-Lipschitz regularity result for X and we show that the Lipschitz constant grows at most linearly in time. As a c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3831e528fac9624f54dc1336e2c0a12c
Publikováno v:
Calculus of Variations and Partial Differential Equations
We study a measure-theoretic notion of connectedness for sets of finite perimeter in the setting of doubling metric measure spaces supporting a weak $(1,1)$-Poincar\'{e} inequality. The two main results we obtain are a decomposition theorem into inde
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a2658e1a1746bf690479a6e38f192091
https://doi.org/10.1007/s00526-020-1725-7
https://doi.org/10.1007/s00526-020-1725-7
Autor:
Stefano Bianchini, Paolo Bonicatto
Publikováno v:
Inventiones mathematicae
Given a vector field $$\rho (1,\mathbf {b}) \in L^1_\mathrm{loc}(\mathbb {R}^+\times \mathbb {R}^{d},\mathbb {R}^{d+1})$$ such that $${{\,\mathrm{div}\,}}_{t,x} (\rho (1,\mathbf {b}))$$ is a measure, we consider the problem of uniqueness of the repre
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::53164b96abcd09821f732377e7fcddda
Publikováno v:
Contemporary Mathematics. Fundamental Directions. 63:418-436
In this note we present a unifying approach for two classes of first order partial differential equations: we introduce the notion of Lagrangian representation in the settings of continuity equation and scalar conservation laws. This yields, on the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::94665a0f118fa8cb8a59676e61235d8f
https://doi.org/10.22363/2413-3639-2017-63-3-418-436
https://doi.org/10.22363/2413-3639-2017-63-3-418-436
Autor:
Stefano Bianchini, Paolo Bonicatto
Publikováno v:
Discrete & Continuous Dynamical Systems-A
We introduce the notion of forward untangled Lagrangian representation of a measure-divergence vector-measure \begin{document}$ \rho(1, {\mathit{\boldsymbol{b}}}) $\end{document} , where \begin{document}$ \rho \in \mathcal{M}^+( \mathbb{R}^{d+1}) $\e
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::de422cf1609bb1e0b20107b334215076
https://doi.org/10.3934/dcds.2020384
https://doi.org/10.3934/dcds.2020384
Autor:
Nikolay A. Gusev, Paolo Bonicatto
Publikováno v:
Rendiconti Lincei-Matematica e Applicazioni
We consider the continuity equation $\partial_t \mu_t + \mathop{\mathrm{div}}(b \mu_t) = 0$, where $\{\mu_t\}_{t \in \mathbb R}$ is a measurable family of (possibily signed) Borel measures on $\mathbb R^d$ and $b \colon \mathbb R \times \mathbb R^d \
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9bc6b185f596d1b60d1c587be096ff38
http://arxiv.org/abs/1809.10216
http://arxiv.org/abs/1809.10216