Geodesic
Estimates for evolutionary partial differential equations in classical function spaces
Forum of Mathematics, Sigma, Tome 11 (2023)

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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. 
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     author = {Alejandro J. Castro and Anders Israelsson and Wolfgang Staubach and Madi Yerlanov},
     title = {Estimates for evolutionary partial differential equations in classical function spaces},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {11},
     year = {2023},
     doi = {10.1017/fms.2023.76},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.76/}
}
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Alejandro J. Castro; Anders Israelsson; Wolfgang Staubach; Madi Yerlanov. Estimates for evolutionary partial differential equations in classical function spaces. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.76

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