Estimates for evolutionary partial differential equations in classical function spaces

Castro A.J. Israelsson A. Staubach W. Yerlanov M.
1 September 2023 Cambridge University Press

Forum of Mathematics, Sigma
2023 #11

We establish new local and global estimates for evolutionary partial differential equations in classical Banach and quasi-Banach spaces that appear most frequently in the theory of partial differential equations. More specifically, we obtain optimal (local in time) estimates for the solution to the Cauchy problem for variable-coefficient evolutionary partial differential equations. The estimates are achieved by introducing the notions of Schrödinger and general oscillatory integral operators with inhomogeneous phase functions and prove sharp local and global regularity results for these in Besov-Lipschitz and Triebel-Lizorkin spaces.

42B20 42B35 42B37 47D06 47D08 35G10 35S30 37L50

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Nazarbayev University, Department of Mathematics, Qabanbay Batyr Ave 53, Astana, 010000, Kazakhstan
Uppsala University, Department of Mathematics, Lägerhyddsvägen 1, Uppsala, 752 37, Sweden
Uppsala University, Department of Mathematics, Lägerhyddsvägen 1, Uppsala, 752 37, Sweden
University of Colorado Boulder, Department of Applied Mathematics, Engineering Center, ECOT 225, 526 UCB, Boulder, 80309-0526, CO, United States

Nazarbayev University
Uppsala University
Uppsala University
University of Colorado Boulder

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