Symmetry properties of solutions to elliptic quasilinear equations have been widely studied in the context of Dirichlet boundary conditions. We show that, in the context of Robin boundary conditions, the symmetry property á la Gidas, Ni, and Nirenberg does not hold in dimension n ≥ 2, even for superharmonic functions, and we provide an explicit example.
A remark on solutions to semilinear equations with Robin boundary conditions / Celentano, Antonio; Masiello, Alba Lia; Paoli, Gloria. - In: ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN. - ISSN 0232-2064. - 43:3(2024), pp. 461-469. [10.4171/zaa/1773]
A remark on solutions to semilinear equations with Robin boundary conditions
Masiello, Alba Lia;Paoli, Gloria
2024
Abstract
Symmetry properties of solutions to elliptic quasilinear equations have been widely studied in the context of Dirichlet boundary conditions. We show that, in the context of Robin boundary conditions, the symmetry property á la Gidas, Ni, and Nirenberg does not hold in dimension n ≥ 2, even for superharmonic functions, and we provide an explicit example.File in questo prodotto:
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