Well-posedness of equations with fractional derivative

作者：Bu Shang Quan^*

来源：Acta Mathematica Sinica-English Series, 2010, 26(7): 1223-1232.

DOI：10.1007/s10114-010-9231-z

• well-posedness
• fractional derivative
• fractional Sobolev spaces
• Fourier multipliers

We study the well-posedness of the equations with fractional derivative D (alpha) u(t) = Au(t)+ f(t), 0 a parts per thousand currency sign t a parts per thousand currency sign 2 pi, where A is a closed operator in a Banach space X, alpha > 0 and D (alpha) is the fractional derivative in the sense of Weyl. Using known results on L (p) -multipliers, we give necessary and/or sufficient conditions for the L (p) -well-posedness of this problem. The conditions we give involve the resolvent of A and the Rademacher boundedness. Corresponding results on the well-posedness of this problem in periodic Besov spaces, periodic Triebel-Lizorkin spaces and periodic Hardy spaces are also obtained.

• 出版日期2010-7
• 单位清华大学