Banach空间中非齐次分数阶抽象柯西问题的Hlder正则性

Hlder Regularity of Fractional Abstract Cauchy Problem with Nonhomogeneous in Banach Space

本文在Banach空间X中考虑相应于线性算子A的α阶抽象Cauchy问题的mild解的Hlder正则性,其中α∈(0,1),算子A生成C_0解析半群.所用方法不同于Clement等人的相应工作,并且对解析半群没有角的限制.得到如下结果:(a)如果非齐次项f∈L^p((0,b),X),1/α<P<∞,则问题的mild解是Hlder连续的;(b)如果f是Hlder连续的且函数u是问题的解,则Au是Hlder连续的.

This paper is concerned with the H51der regularity of the mild solution of the fractional abstract Cauehy problem of order α∈（0,1） associated with a linear operator A in a Banach space X, where A is the generator of an analytic semigroup, and the methods is different than the one in Clement＇s similar work and it is no restriction of angle involved in analytic semigroup. It is shown that （a） if the nonhomogeneous term f∈Lp（（0,b）,X）,1/α〈p〈∞, then the mild solution is Holder continuoas; （b） if f is HSlder continuous and u is the solution, then Au is HSlder continuous.