Semilinear \(p\)-evolution equations in weighted Sobolev spaces

DOI10.1007/978-3-030-61346-4_1zbMath1461.35107OpenAlexW3126767523MaRDI QIDQ2662131

Alessia Ascanelli, Marco Cappiello

Publication date: 9 April 2021

Full work available at URL: https://doi.org/10.1007/978-3-030-61346-4_1

zbMATH Keywords

weighted Sobolev spacespseudo-differential operatorsNash-Moser theoremsemilinear Cauchy problem

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) NLS equations (nonlinear Schrödinger equations) (35Q55) Initial value problems for nonlinear higher-order PDEs (35G25)

Cites Work

• Semilinear \(p\)-evolution equations in Sobolev spaces
• Well-posedness of the Cauchy problem for \(p\)-evolution equations
• Weighted energy estimates for \(p\)-evolution equations in \textit{SG} classes
• The interplay between decay of the data and regularity of the solution in Schrödinger equations
• Log-Lipschitz regularity for SG hyperbolic systems
• Some remarks on the Cauchy problem for Schrödinger type equations
• Operatori pseudo-differenziali in R\(^n\) e applicazioni
• A necessary condition for \(H^\infty \) well-posedness of \(p\)-evolution equations
• The Cauchy problem for Schrödinger type equations
• Schrödinger-type equations in Gelfand-Shilov spaces
• Well-posedness for degenerate Schrödinger equations
• On the Fefferman--Phong inequality and a Wiener-type algebra of pseudodifferential operators
• Some Remarks on Gevrey Well-Posedness for Degenerate Schrödinger Equations
• The inverse function theorem of Nash and Moser
• On positivity of pseudo-differential operators
• Local existence for semilinear weakly hyperbolic equations with time dependent coefficients
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item