Report
Global Lorentz gradient estimates for quasilinear equations with measure data for the strongly singular case: $1
التفاصيل البيبلوغرافية
العنوان:
Global Lorentz gradient estimates for quasilinear equations with measure data for the strongly singular case: $1
المؤلفون:
Le, Cong Nhan, Le, Xuan Truong
سنة النشر:
2020
المجموعة:
Mathematics
مصطلحات موضوعية:
Mathematics - Analysis of PDEs, 35J60, 35J61, 35J62
الوصف:
In this paper, we study the global regularity estimates in Lorentz spaces for gradients of solutions to quasilinear elliptic equations with measure data of the form \begin{eqnarray*} \left\{ \begin{array}{rcl} -{\rm div}(\mathcal{A}(x, \nabla u))&=& \mu \quad \text{in} ~\Omega, u&=&0 \quad \text{on}~ \partial \Omega, \end{array}\right. \end{eqnarray*} where $\mu$ is a finite signed Radon measure in $\Omega$, $\Omega \subset \mathbb{R}^n$ is a bounded domain such that its complement $\mathbb{R}^n\backslash\Omega$ is uniformly $p$-thick and $\mathcal{A}$ is a Carath\'eodory vector valued function satisfying growth and monotonicity conditions for the strongly singular case $1
نوع الوثيقة:
Working Paper
DOI:
10.1142/S021919972050056X
URL الوصول:
http://arxiv.org/abs/2003.11237
رقم الانضمام:
edsarx.2003.11237
قاعدة البيانات:
arXiv
| العنوان: | Global Lorentz gradient estimates for quasilinear equations with measure data for the strongly singular case: $1 |
|---|---|
| المؤلفون: | Le, Cong Nhan, Le, Xuan Truong |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, 35J60, 35J61, 35J62 |
| الوصف: | In this paper, we study the global regularity estimates in Lorentz spaces for gradients of solutions to quasilinear elliptic equations with measure data of the form \begin{eqnarray*} \left\{ \begin{array}{rcl} -{\rm div}(\mathcal{A}(x, \nabla u))&=& \mu \quad \text{in} ~\Omega, u&=&0 \quad \text{on}~ \partial \Omega, \end{array}\right. \end{eqnarray*} where $\mu$ is a finite signed Radon measure in $\Omega$, $\Omega \subset \mathbb{R}^n$ is a bounded domain such that its complement $\mathbb{R}^n\backslash\Omega$ is uniformly $p$-thick and $\mathcal{A}$ is a Carath\'eodory vector valued function satisfying growth and monotonicity conditions for the strongly singular case $1 |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1142/S021919972050056X |
| URL الوصول: | http://arxiv.org/abs/2003.11237 |
| رقم الانضمام: | edsarx.2003.11237 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1142/S021919972050056X |
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