Sobolev Differentiability Properties of Logarithmic Modulus of Real Analytic Functions
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917069798244352 |
|---|---|
| author | Shi, Ziming Zhang, Ruixiang |
| author_facet | Shi, Ziming Zhang, Ruixiang |
| contents | Let $f$ be the germ of a real analytic function at the origin in $\mathbb{R}^n $ for $n \geq 2$, and suppose the codimension of the zero set of $f$ at $\mathbf{0}$ is at least $2$. We show that $\log |f|$ is $W^{1,1}_{\operatorname{loc}}$ near $\mathbf{0}$. In particular, this implies the differential inequality $|\nabla f |\leq V |f|$ holds with $V \in L^1_{\operatorname{loc}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_02159 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Sobolev Differentiability Properties of Logarithmic Modulus of Real Analytic Functions Shi, Ziming Zhang, Ruixiang Classical Analysis and ODEs Primary 26D10, Secondary 26E05, 03C64 Let $f$ be the germ of a real analytic function at the origin in $\mathbb{R}^n $ for $n \geq 2$, and suppose the codimension of the zero set of $f$ at $\mathbf{0}$ is at least $2$. We show that $\log |f|$ is $W^{1,1}_{\operatorname{loc}}$ near $\mathbf{0}$. In particular, this implies the differential inequality $|\nabla f |\leq V |f|$ holds with $V \in L^1_{\operatorname{loc}}$. |
| title | Sobolev Differentiability Properties of Logarithmic Modulus of Real Analytic Functions |
| topic | Classical Analysis and ODEs Primary 26D10, Secondary 26E05, 03C64 |
| url | https://arxiv.org/abs/2205.02159 |