Maximal L^p-regularity for evolution equations governed by non-autonomous forms in weighted spaces

References

• Ouhabaz EM. Analysis of heat equations on domains. Princeton (NJ): Princeton University Press; 2005. (vol. 31, London mathematical society monographs series).
   Google Scholar
• Lions JL. Équations différentielles opérationnelles et problèmes aux limites. Berlin: Springer-Verlag; 1961. (vol. 111, Die Grundlehren der mathematischen wissenschaften).
   Google Scholar
• Ouhabaz EM, Spina C. Maximal regularity for non-autonomous Schrödinger type equations. J Differ Equ. 2010;248(7):1668–1683. doi: 10.1016/j.jde.2009.10.004
   Web of Science ®Google Scholar
• Haak B, Ouhabaz EM. Maximal regularity for non-autonomous evolution equations. Math Ann. 2015;363(3–4):1117–1145. doi: 10.1007/s00208-015-1199-7
   Web of Science ®Google Scholar
• Achache M, Ouhabaz EM. Lions' maximal regularity problem with H12-regularity in time. J Differ Equ. 2019;266:3654–3678. doi: 10.1016/j.jde.2018.09.015
   Web of Science ®Google Scholar
• Fackler S. Non-autonomous maximal Lp-regularity under fractional Sobolev regularity in time. Anal PDE. 2018;11(5):1143–1169. doi: 10.2140/apde
   Web of Science ®Google Scholar
• Arendt W, Dier D, Fackler S, et al. Problem on maximal regularity. Arch Math (Basel). 2017;109(1):59–72. doi: 10.1007/s00013-017-1031-6
   Web of Science ®Google Scholar
• Lasiecka I, Priyasad B, Triggiani R. Uniform stabilization of 3D Navier–Stokes equations in low regularity Besov spaces with finite dimensional, Tangential–Like boundary, localized feedback controllers. Arch Ration Mech Anal. 2021;241(3):1575–1654. doi: 10.1007/s00205-021-01677-w
   Web of Science ®Google Scholar
• Lasiecka I, Priyasad B, Triggiani R. Uniform stabilization of Boussinesq systems in critical -based Sobolev and Besov spaces by finite dimensional interior localized feedback controls. Discrete Contin Dyn Syst – B. 2020;25(10):4071–4117. doi: 10.3934/dcdsb.2020187
   Google Scholar
• Lasiecka I, Priyasad B, Triggiani R. Maximal Lp-regularity for an abstract evolution equation with applications to closed-loop boundary feedback control problems. J Differ Equ. 2021;294:60–87. doi: 10.1016/j.jde.2021.05.046
   Web of Science ®Google Scholar
• Prüss J, Simonett G. Maximal regularity for evolution equations in weighted Lp-spaces. Arch Math. 2004;82(5):415–431.
   Web of Science ®Google Scholar
• Simon J. Sobolev, Besov and Nikolskii fractional spaces: imbeddings and comparisons for vector valued spaces on an interval. Ann Mat Pura Appl. 1990;157(4):117–148.
   Google Scholar
• Gallarati C. Maximal regularity for parabolic equations with measurable dependence on time and applications [PhD thesis]. Delft University of Technology; 2017.
   Google Scholar
• Diestel J, Uhl JJ. Jr. Vector measures. Providence (RI): American Mathematical Society; 1977.
   Google Scholar
• Lang S. Complex analysis. 4th ed. Berlin: Springer; 1999. (Vol. 103, Graduate texts in mathematics).
   Google Scholar
• Lunardi A. Interpolation theory. Second. Appunti. Scuola normale superiore di pisa (Nuova Serie). Pisa: Edizioni della Normale; 2009. (Lecture notes: Scuola normale superiore di pisa).
   Google Scholar
• Achache M, Hossni T. Maximal regularity for non-autonomous Cauchy problems in weighted spaces. Electron J Differ Equ. 2020;2020(1):1–24. doi: 10.1186/s13662-019-2438-0
   Google Scholar
• Bergh J, Lofstrom J. Interpolation spaces: an introduction: 223 (Grundlehren der mathematischen wissenschaften). Berlin: Springer-Verlag; 1976. p. 207.
   Google Scholar
• Triebel H. Interpolation theory, function spaces, differential operators. 2nd ed. Heidelberg: Johann Ambrosius Barth; 1995.
   Google Scholar
• Batty C, Chill R, Srivastava S. Maximal regularity in interpolation spaces for second-order Cauchy problems. In: Arendt W, Chill R, Tomilov Y, editors. Operator semigroups meet complex analysis, harmonic analysis and mathematical physics. Vol. 250, Operator theory: advances and applications, Basel. Springer International Publishing; 2015. p. 49–66.
   Google Scholar