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pro vyhledávání: '"Biagi, Stefano"'
In this paper we study the effect of the Hardy potential on existence, uniqueness and optimal summability of solutions of the mixed local-nonlocal elliptic problem $$-\Delta u + (-\Delta)^s u - \gamma \frac{u}{|x|^2}=f \text{ in } \Omega, \ u=0 \text
Externí odkaz:
http://arxiv.org/abs/2407.06763
We are concerned with the Cauchy problem for the semilinear parabolic equation driven by the mixed local-nonlocal operator $\mathcal{L} = -\Delta+(-\Delta)^s$, with a power-like source term. We show that the so-called Fujita phenomenon holds, and the
Externí odkaz:
http://arxiv.org/abs/2406.17731
Autor:
Biagi, Stefano, Punzo, Fabio
We investigate the validity of the Phragm\`en-Lindel\"of principle for a class of elliptic equations with a potential, posed on infinite graphs. Consequently, we get uniqueness, in the class of solutions satisfying a suitable growth condition at infi
Externí odkaz:
http://arxiv.org/abs/2406.06505
Autor:
Biagi, Stefano, Bramanti, Marco
We consider Kolmogorov-Fokker-Planck operators of the form $$ \mathcal{L}u=\sum_{i,j=1}^{q}a_{ij}(x,t)u_{x_{i}x_{j}}+\sum_{k,j=1}^{N} b_{jk}x_{k}u_{x_{j}}-\partial_{t}u, $$ with $\left( x,t\right) \in\mathbb{R}^{N+1},N\geq q\geq1$. We assume that $a_
Externí odkaz:
http://arxiv.org/abs/2405.09358
Autor:
Biagi, Stefano, Vecchi, Eugenio
We prove the existence of a second positive weak solution for mixed local-nonlocal critical semilinear elliptic problems with a sublinear perturbation in the spirit of [Ambrosetti, Brezis, Cerami, 1994].
Comment: arXiv admin note: text overlap w
Comment: arXiv admin note: text overlap w
Externí odkaz:
http://arxiv.org/abs/2403.18424
Autor:
Biagi, Stefano, Bramanti, Marco
We consider a class of nonvariational degenerate elliptic operators of the kind \[ Lu=\sum_{i,j=1}^{m}a_{ij}\left( x\right) X_{i}X_{j}u \] where $\left\{ a_{ij}\left( x\right) \right\} _{i,j=1}^{m}$ is a symmetric uniformly positive matrix of bounded
Externí odkaz:
http://arxiv.org/abs/2312.15367
Autor:
Biagi Stefano, Bramanti Marco
Publikováno v:
Analysis and Geometry in Metric Spaces, Vol 12, Iss 1, Pp 734-771 (2024)
We consider degenerate Kolmogorov-Fokker-Planck operators ℒu=∑i,j=1qaij(x,t)uxixj+∑k,j=1Nbjkxkuxj−ut,{\mathcal{ {\mathcal L} }}u=\mathop{\sum }\limits_{i,j=1}^{q}{a}_{ij}\left(x,t){u}_{{x}_{i}{x}_{j}}+\mathop{\sum }\limits_{k,j=1}^{N}{b}_{jk}
Externí odkaz:
https://doaj.org/article/df20c746c11f43dab6e0f930998d5f20
Autor:
Biagi, Stefano, Vecchi, Eugenio
We prove the existence of at least two positive weak solutions for mixed local-nonlocal singular and critical semilinear elliptic problems in the spirit of [Haitao, 2003], extending the recent results in [Garain, 2023] concerning singular problems an
Externí odkaz:
http://arxiv.org/abs/2308.09794
We study mixed local and nonlocal elliptic equation with a variable coefficient $\rho$. Under suitable assumptions on the behaviour at infinity of $\rho$, we obtain uniqueness of solutions belonging to certain weighted Lebsgue spaces, with a weight d
Externí odkaz:
http://arxiv.org/abs/2307.02209
We consider degenerate KFP operators \[ Lu=\sum_{i,j=1}^{m_{0}}a_{ij}(x,t)\partial_{x_{i}x_{j}}^{2}u+\sum_{k,j=1}^{N}b_{jk}x_{k}\partial_{x_{j}}u-\partial_{t}u\equiv\sum_{i,j=1}^{m_{0}}a_{ij}(x,t)\partial_{x_{i}x_{j}}^{2}u+Yu \] ($(x,t)\in\mathbb{R}^
Externí odkaz:
http://arxiv.org/abs/2305.11641