ABSTRACT
In this chapter, taking advantage of the results proved in all the previous chapters, we show that the semigroups considered in Chapters 6 to 9 are analytic and we characterize the interpolations spaces of order α and 1 + α https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429262593/03624a6d-a4e5-45fb-ba52-c2b8f08b80c3/content/math14_1.tif"/> for every α ∈ ( 0 , 1 ) ∖ { 1 / 2 } https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429262593/03624a6d-a4e5-45fb-ba52-c2b8f08b80c3/content/math14_2.tif"/> . Moreover, using tools from semigroup theory we provide the proof of the regularity results in Section 7.4. This to further enlighten the connections between parabolic equations and analytic semigroups of bounded operators.
