A priori estimates for higher order hyperbolic equations

DOI10.1007/BF02571728zbMath0790.35063MaRDI QIDQ1323464

Mitsuru Sugimoto

Publication date: 26 June 1994

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174626

zbMATH Keywords

Cauchy problema priori estimatestrictly hyperbolic equation\(L^ p\)-\(L^{p'}\)-estimategeometrical properties of the characteristics

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Geometric theory, characteristics, transformations in context of PDEs (35A30) Initial value problems for higher-order hyperbolic equations (35L30)

Related Items (11)

Estimates for hyperbolic equations with non-convex characteristics ⋮ On \(t\)-dependent hyperbolic systems. II. ⋮ 𝐿^{𝑝}→𝐿^{𝑞} regularity of Fourier integral operators with caustics ⋮ Pointwise van der Corput lemma for functions of several variables ⋮ \(L^p-L^q\) estimates for higher order perturbed hyperbolic equation ⋮ Sharp estimates for a class of hyperbolic pseudo-differential equations ⋮ Dispersive estimates for hyperbolic systems with time-dependent coefficients ⋮ Time decay for hyperbolic equations with homogeneous symbols ⋮ One application of Floquet's theory toLp-Lq estimates for hyperbolic equations with very fast oscillations ⋮ Estimates for hyperbolic equations of space dimension 3 ⋮ A remark on the asymptotic properties of eigenvalues and the lattice point problem

Cites Work

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• A priori estimates for the wave equation and some applications
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• 𝐿^{𝑝} boundedness of Fourier integral operators
• On the Asymptotic Behavior of the Fourier Transform of the Indicator Function of a Convex Set
• Convolutions with Kernels Having Singularities on a Sphere

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