论文标题
在单数和退化椭圆问题中的吸收项的正则效应
Regularizing effect of absorption terms in singular and degenerate elliptic problems
论文作者
论文摘要
在本文中，我们研究解决方案的存在和规律性，以解决以下单一问题\ begin {equation} \ left \ {\ oken {array} {lll} {lll}＆ - \ displayStyle \ displayStyle \ mbox {div} \ big（a（a（a（a）） = \ frac {f} {u^γ}＆\ mbox {in}ω\\＆u> 0＆\ mbox {in}ω\\ u = 0＆\ mbox {on}ΔΩ \ end {equation}证明，在具有退化的胁迫性的椭圆运算符的情况下，较低阶段$ u | u | u | u | u |^{s-1} $对解决方案具有一些正规化的影响。
In this paper we study the existence and regularity of solutions to the following singular problem \begin{equation} \left\{ \begin{array}{lll} &-\displaystyle\mbox{div} \big(a(x,u)|\nabla u|^{p-2}|\nabla u|\big) + |u|^{s-1}u =\frac{f}{u^γ} &\mbox{ in } Ω\\ &u>0 &\mbox{ in }Ω\\ &u=0 &\mbox{ on } δΩ\end{array} \right. \end{equation} proving that the lower order term $u|u|^{s-1}$ has some regularizing effects on the solutions in the case of an elliptic operator with degenerate coercivity.
