论文标题
圆锥形域中的广义扩散问题，第一部分
Generalized diffusion problems in a conical domain, part I
论文作者
论文摘要
本文的目的（由两个部分组成）是对有限的锥形域中的$ l^p $ - 空格的广义分散操作员的研究，该方程设置为有限的圆锥域$ s_ {ω，ρ} $ of Angle $ω> 0 $和半径$和半径$ pus $ p $ punius $ρ> 0 $ in $ \ \ \ \ \ \ \ \ \ \ \ mathbb {r}^2 $。第一部分致力于锥体顶部附近的解决方案的行为，这在加权的Sobolev空间中完全描述了$ W^{4，P} _ {3- \ frac {1} {p} {p}}}}}（s_ {ω，ρ}，ρ}）$，请参见Theorem 2.2。
The purpose of this article (composed of two parts) is the study of the generalized dispersal operator of a reaction-diffusion equation in $L^p$-spaces set in the finite conical domain $S_{ω,ρ}$ of angle $ω>0$ and radius $ρ>0$ in $\mathbb{R}^2$. This first part is devoted to the behaviour of the solution near the top of the cone which is completely described in the weighted Sobolev space $W^{4,p}_{3-\frac{1}{p}}(S_{ω,ρ})$, see Theorem 2.2.
