Fully nonlinear degenerate equations with applications to Grad equations
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909956781899776 |
|---|---|
| author | Oza, Priyank |
| author_facet | Oza, Priyank |
| contents | We consider a class of degenerate elliptic fully nonlinear equations with applications to Grad equations:
\begin{align}
\begin{cases}
|Du|^γ\mathcal{M}_{λ,Λ}^+\big(D^2u(x)\big)=f\big(|u\geq u(x)|\big) &\text{ in }Ω,
u=g &\text{ on }\partialΩ,
\end{cases}
\end{align}
where $γ\geq 1$ is a constant, $Ω$ is a bounded domain in $\mathbb{R}^N$ with $C^{1,1}$ boundary. We prove the existence of a $W^{2,p}$-viscosity solution to the above equation, which degenerates when the gradient of the solution vanishes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11255 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fully nonlinear degenerate equations with applications to Grad equations Oza, Priyank Analysis of PDEs 35J25, 35J60, 35J70, 35D40 We consider a class of degenerate elliptic fully nonlinear equations with applications to Grad equations: \begin{align} \begin{cases} |Du|^γ\mathcal{M}_{λ,Λ}^+\big(D^2u(x)\big)=f\big(|u\geq u(x)|\big) &\text{ in }Ω, u=g &\text{ on }\partialΩ, \end{cases} \end{align} where $γ\geq 1$ is a constant, $Ω$ is a bounded domain in $\mathbb{R}^N$ with $C^{1,1}$ boundary. We prove the existence of a $W^{2,p}$-viscosity solution to the above equation, which degenerates when the gradient of the solution vanishes. |
| title | Fully nonlinear degenerate equations with applications to Grad equations |
| topic | Analysis of PDEs 35J25, 35J60, 35J70, 35D40 |
| url | https://arxiv.org/abs/2303.11255 |