Some minimum principles for a class of nonlinear elliptic problems in divergence form
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912964793073664 |
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| author | Enache, Cristian Lopez, Rafael |
| author_facet | Enache, Cristian Lopez, Rafael |
| contents | In this paper we study a general class of nonlinear elliptic problems in divergence form. First, we prove that the solutions to these problems satisfy a convexity property when the given domain is strictly convex. Then, making use of this convexity property, we develop some minimum principles for an appropriate $P$-function, in the sense of L.~E.~Payne. Finally, this new minimum principle is applied to find a priori estimates for the solutions, in terms of the mean curvature of the boundary of the underlying domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12931 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Some minimum principles for a class of nonlinear elliptic problems in divergence form Enache, Cristian Lopez, Rafael Analysis of PDEs In this paper we study a general class of nonlinear elliptic problems in divergence form. First, we prove that the solutions to these problems satisfy a convexity property when the given domain is strictly convex. Then, making use of this convexity property, we develop some minimum principles for an appropriate $P$-function, in the sense of L.~E.~Payne. Finally, this new minimum principle is applied to find a priori estimates for the solutions, in terms of the mean curvature of the boundary of the underlying domain. |
| title | Some minimum principles for a class of nonlinear elliptic problems in divergence form |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.12931 |