Fully Nonlinear Singularly perturbed models with non-homogeneous degeneracy
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2021
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| _version_ | 1866910411187552256 |
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| author | Silva, João V. Júnior, Elzon C. Ricarte, Gleydson C. |
| author_facet | Silva, João V. Júnior, Elzon C. Ricarte, Gleydson C. |
| contents | In our work we study non-variational, nonlinear singularly perturbed elliptic models enjoying a double degeneracy character with prescribed boundary value in a domain. In such a scenario, we establish the existence of solutions. We also prove that solutions are locally (uniformly) Lipschitz continuous, and they grow in a linear fashion. Moreover, solutions and their free boundaries possess a sort of measure-theoretic and weak geometric properties. Moreover, for a restricted class of non-linearities, we prove the finiteness of the (N-1)-dimensional Hausdorff measure of level sets. We also address a complete analysis concerning the asymptotic limit as the singular parameter, which is related to one-phase solutions of inhomogeneous nonlinear free boundary problems in flame propagation and combustion theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_08664 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Fully Nonlinear Singularly perturbed models with non-homogeneous degeneracy Silva, João V. Júnior, Elzon C. Ricarte, Gleydson C. Analysis of PDEs In our work we study non-variational, nonlinear singularly perturbed elliptic models enjoying a double degeneracy character with prescribed boundary value in a domain. In such a scenario, we establish the existence of solutions. We also prove that solutions are locally (uniformly) Lipschitz continuous, and they grow in a linear fashion. Moreover, solutions and their free boundaries possess a sort of measure-theoretic and weak geometric properties. Moreover, for a restricted class of non-linearities, we prove the finiteness of the (N-1)-dimensional Hausdorff measure of level sets. We also address a complete analysis concerning the asymptotic limit as the singular parameter, which is related to one-phase solutions of inhomogeneous nonlinear free boundary problems in flame propagation and combustion theory. |
| title | Fully Nonlinear Singularly perturbed models with non-homogeneous degeneracy |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2101.08664 |