The concept of mapped coercivity for nonlinear operators in Banach spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866915205662900224 |
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| author | Becker, Roland Braack, Malte |
| author_facet | Becker, Roland Braack, Malte |
| contents | We provide a concise proof of existence for nonlinear operator equations in separable Banach spaces. Notably, the operator is not assumed to be monotone. Instead, our main hypotheses consist of a continuity assumption and a generalized coercivity property. Mapped coercivity is a generalization of the usual coercivity property for nonlinear operators. In the case of linear operators, we recover linear coercivity and the traditional inf-sup condition. To illustrate the applicability of this general concept, we apply it to semi-linear elliptic problems and the Navier-Stokes equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_16783 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The concept of mapped coercivity for nonlinear operators in Banach spaces Becker, Roland Braack, Malte Analysis of PDEs Functional Analysis 35J60, 35J61, 35J20, 46T99, 47H99, 47J05, 47J30 We provide a concise proof of existence for nonlinear operator equations in separable Banach spaces. Notably, the operator is not assumed to be monotone. Instead, our main hypotheses consist of a continuity assumption and a generalized coercivity property. Mapped coercivity is a generalization of the usual coercivity property for nonlinear operators. In the case of linear operators, we recover linear coercivity and the traditional inf-sup condition. To illustrate the applicability of this general concept, we apply it to semi-linear elliptic problems and the Navier-Stokes equations. |
| title | The concept of mapped coercivity for nonlinear operators in Banach spaces |
| topic | Analysis of PDEs Functional Analysis 35J60, 35J61, 35J20, 46T99, 47H99, 47J05, 47J30 |
| url | https://arxiv.org/abs/2305.16783 |