On Some Degenerate Elliptic Equations Arising in Geometric Problems
| Autor: | Fabiana Leoni, Antonio Vitolo, I. Capuzzo Dolcetta |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Pure mathematics degenerate Pucci operators partial laplacian generalized principal eigenvalue entire subsolutions Applied Mathematics General Mathematics 010102 general mathematics Degenerate energy levels Mathematics (all) Term (logic) 01 natural sciences 010101 applied mathematics Nonlinear system Elliptic operator Maximum principle 0101 mathematics Equivalence (measure theory) Eigenvalues and eigenvectors Mathematics Sign (mathematics) |
| Zdroj: | Journal of Mathematical Sciences. 233:446-461 |
| ISSN: | 1573-8795 1072-3374 |
| DOI: | 10.1007/s10958-018-3937-3 |
| Popis: | We consider some fully nonlinear degenerate elliptic operators and we investigate the validity of certain properties related to the maximum principle. In particular, we establish the equivalence between the sign propagation property and the strict positivity of a suitably defined generalized principal eigenvalue. Furthermore, we show that even in the degenerate case considered in the present paper, the well-known condition introduced by Keller–Osserman on the zero-order term is necessary and sufficient for the existence of entire weak subsolutions. |
| Databáze: | OpenAIRE |
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