On Schrödinger type evolution equations with non-Lipschitz coefficients

DOI10.1007/s10231-010-0167-9zbMath1242.35099OpenAlexW1977754851MaRDI QIDQ415437

Massimo Cicognani, Michael Reissig

Publication date: 8 May 2012

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-010-0167-9

zbMATH Keywords

well-posednessSchrödinger-type operatorsEuler-Bernoulli vibrating beamreal characteristics

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Initial value problems for linear higher-order PDEs (35G10)

Related Items (5)

Semilinear \(p\)-evolution equations in Sobolev spaces ⋮ Well-posedness of the Cauchy problem for \(p\)-evolution systems of pseudo-differential operators ⋮ Well-posedness of the Cauchy problem for \(p\)-evolution equations ⋮ The Global Cauchy Problem for the Plate Equation in Weighted Sobolev Spaces ⋮ Weighted energy estimates for \(p\)-evolution equations in \textit{SG} classes

Cites Work

• The global Cauchy problem for a vibrating beam equation
• Loss of regularity for \(p\)-evolution type models
• Some remarks on the Cauchy problem for Schrödinger type equations
• Local uniqueness in the Cauchy problem for second order elliptic equations with non-Lipschitzian coefficients
• The Cauchy problem for Schrödinger type equations
• Sharp regularity of the coefficients in the Cauchy problem for a class of evolution equations
• Remarks on pseudo-differential operators
• The Cauchy problem for 𝑝-evolution equations

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