A Brezis-Oswald approach for mixed local and nonlocal operator

By Stefano Biagi, Dimitri Mugnai, E. Vecchi. Communications in Contemporary Mathematics, 2021

65 citations recorded by the source corpus.

. In this paper we provide necessary and suﬃcient conditions for the existence of a unique positive weak solution for some sublinear Dirichlet problems driven by the sum of a quasilinear local and a nonlocal operator, i.e., L p,s = − ∆ p + ( − ∆) sp . Our main result is resemblant to the celebrated work by Brezis–Oswald [11]. In addition, we prove a regularity result of independent interest.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/d6f3d459a97432f3549634e6330353b01b7bd379

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

A Brezis-Nirenberg type result for mixed local and nonlocal operators (2022, unknown): “…U t,x 0 } is as in Remark 3.1-(4), we have for some C > 0, therefore (up to renaming C line after line) Moreover, recalling that by arguing as in the proof of Theorem 1.1 we have From this, since U = U 1 , 0 is an optimal function in the classical Sobolev inequality (and since s < 1), by letting t…”
A Faber-Krahn inequality for mixed local and nonlocal operators (2021, background): “We want to stress that one can get almost everywhere positivity of u 0 by means of the strong maximum principle for weak solutions proved in [9,14].”