An elliptic equation with power nonlinearity and degenerate coercivity
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910613991587840 |
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| author | da Silva, Genival |
| author_facet | da Silva, Genival |
| contents | We discuss the existence and regularity of solutions to the following Dirichlet problem: $$\begin{equation} \begin{cases} -\textrm{div}\left(\frac{Du}{(1+|u|)^θ}\right)= -\textrm{div}\left(u^γE(x)\right)+f(x) \qquad & \mbox{in } Ω,\\ u (x) = 0 & \mbox{on } \partial Ω, \end{cases} \end{equation}$$ where $θ,γ>0$. An interesting feature of this problem is the interplay between the two nonlinearities, the degeneracy and the power nonlinearity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_13182 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An elliptic equation with power nonlinearity and degenerate coercivity da Silva, Genival Analysis of PDEs 35J70, 35J15, 35B65, 35A01 We discuss the existence and regularity of solutions to the following Dirichlet problem: $$\begin{equation} \begin{cases} -\textrm{div}\left(\frac{Du}{(1+|u|)^θ}\right)= -\textrm{div}\left(u^γE(x)\right)+f(x) \qquad & \mbox{in } Ω,\\ u (x) = 0 & \mbox{on } \partial Ω, \end{cases} \end{equation}$$ where $θ,γ>0$. An interesting feature of this problem is the interplay between the two nonlinearities, the degeneracy and the power nonlinearity. |
| title | An elliptic equation with power nonlinearity and degenerate coercivity |
| topic | Analysis of PDEs 35J70, 35J15, 35B65, 35A01 |
| url | https://arxiv.org/abs/2409.13182 |