由具奇异系数的强椭圆微分算子生成的解析半群

ANALYTIC SEMIGROUPS GENERATED BY STRONGLY ELLIPTIC DIFFERENTIAL OPERATORS WITH SINGULAR COEFFICIENTS

本文提出了低阶项系数具一定奇异性的高阶强椭圆微分算子生成解析半群的条 件,其包含了低阶项系数属于Schecter位势类的情形.特别地,低阶项系数属于LP(Rn) 的情形也在其中.作为应用,得到低阶项系数属于LP(Rn)的强椭圆算子的相应半群生 成,且p还可取到一些临界值.

We show in this paper the conditionthat strongly elliptic differential operators with singular lower order coefficients belonging to a class of measurable functions which includes the Schecter potential class Mσ,τ,q generate analytic semigroups, particularly, the class includes Lp(Rn). As an application, we obtain a result for Lp(Rn) lower order coefficients, where p can be taken as some critical values.