Representation of Solutions and Regularity Properties for Weakly Hyperbolic Systems
Regularity properties of generic hyperbolic systems with diagonalizable principal part will be established in Lp and other function spaces. Sharp regularity of solutions will be discussed. Applications will be given to solutions of scalar weakly hyperbolic equations with non-involutive characteristics. Established representation of solutions and its properties allow to derive spectral asymptotics for elliptic systems with diagonalizable principal part.
KeywordsHyperbolic systems elliptic systems spectral asymptotics regularity of solutions
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- Y. Colin de Verdière, The level crossing problem in semi-classical analysis, I: Symmetric case, II: The Hermitian case, Preprints.Google Scholar
- V. Ya. Ivrii, Microlocal Analysis and Precise Spectral Asymptotics, Springer Monographs in Mathematics. Springer-Verlag, Berlin, 1998.Google Scholar
- I. Kamotski and M. Ruzhansky, Representation of solutions and regularity properties for weakly hyperbolic systems, Funct. Anal. Applic., to appear.Google Scholar
- I. Kamotski and M. Ruzhansky, Regularity properties, representation of solutions and spectral asymptotics of systems with multiplicities, Preprint, arXiv:math.AP/0402203.Google Scholar
- H. Kumano-go, Pseudo-Differential operators. MIT press, Cambridge, Mass. London, 1981.Google Scholar
- Yu. Safarov and D. Vassiliev, The Asymptotic Distribution of Eigenvalues of Partial Differential Operators. Translations of Mathematical Monographs 155 AMS, Providence, RI, 1997.Google Scholar