Linear theory for a mixed operator with Neumann conditions

By Serena Dipierro, Edoardo Proietti Lippi, Enrico Valdinoci. Asymptotic Analysis, 2020

54 citations recorded by the source corpus.

We consider here a new type of mixed local and nonlocal equation under suitable Neumann conditions. We discuss the spectral properties associated to a weighted eigenvalue problem and present a global bound for subsolutions. The Neumann condition that we take into account comprises, as a particular case, the one that has been recently introduced in (Rev. Mat. Iberoam. 33(2) (2017), 377–416). Also, the results that we present here find a natural application to a logistic equation motivated by biological problems that has been recently considered in (Dipierro, Proietti Lippi and Valdinoci (2021)).

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7075833d21daf7bf9b14bfa43e09e216efc3eb02

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Citations in the corpus

Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations (2022, background): “Local boundedness is also established in Dipierro-Proietti Lippi-Valdinoci [20].”
Regularity results for solutions of mixed local and nonlocal elliptic equations (2022, background): “Moreover, mixed operators have recently received a great attention from different points of view, including regularity theory [2, 3, 8, 10, 12, 14, 15, 17, 25], existence and non-existence results [1, 6, 28], eigenvalue problems [13, 16, 22], shape optimization and calculus of variations [7, 11], sy”
Mixed local and nonlocal Sobolev inequalities with extremal and associated quasilinear singular elliptic problems (2021, methodology): “Furthermore, existence, regularity, symmetry and maximum principles along various qualitative properties of solutions have been recently investigated by Biagi-DipierroValdinoci-Vecchi [12, 13], Dipierro-Proietti Lippi-Valdinoci [35, 36], Biagi-Mugnai-Vecchi [15], Dipierro-Ros-Oton-Serra-Valdinoci [3”
A Faber-Krahn inequality for mixed local and nonlocal operators (2021, methodology): “(4.29) Furthermore, using the isoperimetric inequality we see that As a result, we obtain that 1) | .”
On the regularity theory for mixed local and nonlocal quasilinear elliptic equations (2021, methodology): “16) have recently been studied by Biagi-Dipierro-Valdinoci-Vecchi [6,7], Dipierro-Proietti Lippi-Valdinoci [22,23] and Dipierro-Ros-Oton-Serra-Valdinoci [24].”
A Brezis-Oswald approach for mixed local and nonlocal operator (2021, unknown): “Problems driven by operators like Lp,s have raised a certain interest in the last few years, both for the mathematical complications that the combination of two so different operators imply and for the wide range of applications, see for instance [5, 4, 6, 12, 13, 15, 16] and the references therein.”