Regularity for Fully Nonlinear Elliptic Equations with Natural Growth in Gradient and Singular Nonlinearity
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929336799461376 |
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| author | Mallick, Mohan Verma, Ram Baran |
| author_facet | Mallick, Mohan Verma, Ram Baran |
| contents | In this article we consider the following boundary value problem
\begin{equation*}\label{abs} \left\{ \begin{aligned} F(x,u,Du,D^{2}u)+c(x)u+ p(x)u^{-α}&=0~\text{in}~Ω\\ u&=0~~\text{on}~~\partialΩ, \end{aligned} \right. \end{equation*} where $Ω$ is a bounded and $C^{2}$ smooth domain in $\mathbb{R}^N$ and $F$ has superlinear growth in gradient and $c(c)<-c_{0}$ for some positive constant $c_{0}.$ Here, we studies the boundary behaviour of the solutions to above equation and establishes the global regularity result similar to one established in [12,16] with linear growth in gradient. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_03791 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regularity for Fully Nonlinear Elliptic Equations with Natural Growth in Gradient and Singular Nonlinearity Mallick, Mohan Verma, Ram Baran Analysis of PDEs In this article we consider the following boundary value problem \begin{equation*}\label{abs} \left\{ \begin{aligned} F(x,u,Du,D^{2}u)+c(x)u+ p(x)u^{-α}&=0~\text{in}~Ω\\ u&=0~~\text{on}~~\partialΩ, \end{aligned} \right. \end{equation*} where $Ω$ is a bounded and $C^{2}$ smooth domain in $\mathbb{R}^N$ and $F$ has superlinear growth in gradient and $c(c)<-c_{0}$ for some positive constant $c_{0}.$ Here, we studies the boundary behaviour of the solutions to above equation and establishes the global regularity result similar to one established in [12,16] with linear growth in gradient. |
| title | Regularity for Fully Nonlinear Elliptic Equations with Natural Growth in Gradient and Singular Nonlinearity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.03791 |