arXiv
Open Access
2017
Global Marcinkiewicz estimates for nonlinear parabolic equations with nonsmooth coefficients
The Anh Bui
Xuan Thinh Duong
Abstrak
Consider the parabolic equation with measure data \begin{equation*} \left\{ \begin{aligned} &u_t-{\rm div} \mathbf{a}(D u,x,t)=μ&\text{in}& \quad Ω_T, &u=0 \quad &\text{on}& \quad \partial_pΩ_T, \end{aligned}\right. \end{equation*} where $Ω$ is a bounded domain in $\mathbb{R}^n$, $Ω_T=Ω\times (0,T)$, $\partial_pΩ_T=(\partialΩ\times (0,T))\cup (Ω\times\{0\})$, and $μ$ is a signed Borel measure with finite total mass. Assume that the nonlinearity ${\bf a}$ satisfies a small BMO-seminorm condition, and $Ω$ is a Reifenberg flat domain. This paper proves a global Marcinkiewicz estimate for the SOLA (Solution Obtained as Limits of Approximation) to the parabolic equation.
Topik & Kata Kunci
Penulis (2)
T
The Anh Bui
X
Xuan Thinh Duong
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2017
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓