论文标题
推断椭圆规则和应用于半导体的范鸟杆系统
Extrapolated Elliptic Regularity and Application to the van Roosbroeck system of Semiconductors
论文作者
论文摘要
In this paper we present a general extrapolated elliptic regularity result for second order differential operators in divergence form on fractional Sobolev-type spaces of negative order $X^{s-1,q}_D(Ω)$ for $s > 0$ small, including mixed boundary conditions and with a fully nonsmooth geometry of $Ω$ and the Dirichlet boundary part $D$.我们希望结果能在非线性抛物线方程分析中找到应用程序，尤其是对于准线性问题或处理方程耦合系统时。为了证明我们的结果的有用性，我们为半导体设备的van Roosbroeck系统提供了新的局部时间和独特性证明，这比已经建立的证据要简单得多。
In this paper we present a general extrapolated elliptic regularity result for second order differential operators in divergence form on fractional Sobolev-type spaces of negative order $X^{s-1,q}_D(Ω)$ for $s > 0$ small, including mixed boundary conditions and with a fully nonsmooth geometry of $Ω$ and the Dirichlet boundary part $D$. We expect the result to find applications in the analysis of nonlinear parabolic equations, in particular for quasilinear problems or when treating coupled systems of equations. To demonstrate the usefulness of our result, we give a new proof of local-in-time existence and uniqueness for the van Roosbroeck system for semiconductor devices which is much simpler than already established proofs.
