Coupling local and nonlocal equations with Neumann boundary conditions


  • Gabriel Acosta Departamento de Matemática, FCEyN, Universidad de Buenos Aires & IMAS CONICET, Pabellón I, Ciudad Universitaria, 1428 Buenos Aires, Argentina
  • Francisco Bersetche Departamento de Matemática, FCEyN, Universidad de Buenos Aires & IMAS CONICET, Pabellón I, Ciudad Universitaria, 1428 Buenos Aires, Argentina
  • Julio D. Rossi Departamento de Matemática, FCEyN, Universidad de Buenos Aires & IMAS CONICET, Pabellón I, Ciudad Universitaria, 1428 Buenos Aires, Argentina



We introduce two different ways of coupling local and nonlocal equations with Neumann boundary conditions in such a way that the resulting model is naturally associated with an energy functional. For these two models we prove that there is a minimizer of the resulting energy that is unique modulo adding a constant.


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