• Corpus ID: 238743957

Mixed local-nonlocal operators: maximum principles, eigenvalue problems and their applications

  title={Mixed local-nonlocal operators: maximum principles, eigenvalue problems and their applications},
  author={Anup Biswas and Mitesh Modasiya},
In this article we consider a class of non-degenerate elliptic operators obtained by superpositioning the Laplacian and a general nonlocal operator. We study the existence-uniqueness results for Dirichlet boundary value problems, maximum principles and generalized eigenvalue problems. As applications to these results, we obtain Faber-Krahn inequality and a one-dimensional symmetry result related to the Gibbons’ conjecture. The latter results substantially extend the recent results of Biagi et… 


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