Sharp regularity theory for second order hyperbolic equations of Neumann type

Irena Lasiecka; Roberto Triggiani

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1989)

  • Volume: 83, Issue: 1, page 109-113
  • ISSN: 1120-6330

Abstract

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This note provides sharp regularity results for general, time-independent, second order, hyperbolic equations with non-homogeneous data of Neumann type.

How to cite

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Lasiecka, Irena, and Triggiani, Roberto. "Sharp regularity theory for second order hyperbolic equations of Neumann type." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 83.1 (1989): 109-113. <http://eudml.org/doc/287365>.

@article{Lasiecka1989,
abstract = {This note provides sharp regularity results for general, time-independent, second order, hyperbolic equations with non-homogeneous data of Neumann type.},
author = {Lasiecka, Irena, Triggiani, Roberto},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Hyperbolic partial differential equations; mixed problem; general, time-independent, second order hyperbolic equations; non-homogeneous data},
language = {eng},
month = {12},
number = {1},
pages = {109-113},
publisher = {Accademia Nazionale dei Lincei},
title = {Sharp regularity theory for second order hyperbolic equations of Neumann type},
url = {http://eudml.org/doc/287365},
volume = {83},
year = {1989},
}

TY - JOUR
AU - Lasiecka, Irena
AU - Triggiani, Roberto
TI - Sharp regularity theory for second order hyperbolic equations of Neumann type
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1989/12//
PB - Accademia Nazionale dei Lincei
VL - 83
IS - 1
SP - 109
EP - 113
AB - This note provides sharp regularity results for general, time-independent, second order, hyperbolic equations with non-homogeneous data of Neumann type.
LA - eng
KW - Hyperbolic partial differential equations; mixed problem; general, time-independent, second order hyperbolic equations; non-homogeneous data
UR - http://eudml.org/doc/287365
ER -

References

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  1. LIONS, J.L., private communication, May 1984. 
  2. LIONS, J.L. and MAGENES, E., 1972. Nonhomogeneous boundary value problems and applications. Vols. I, II, Springer-Verlag, Berlin-Heidelberg-New York. Zbl0223.35039
  3. LASIECKA, I. and TRIGGIANI, R., 1981. A cosine operator approach to modelling L 2 , T ; L 2 ⁢ ( Γ ) -boundary input hyperbolic equations. Applied Mathem. & Optimiz., 7: 35-93. Zbl0473.35022MR600559DOI10.1007/BF01442108
  4. LASIECKA, I. and TRIGGIANI, R., 1983. Regularity of hyperbolic equations under L 2 , T ; L 2 ⁢ ( Γ ) -boundary terms. Applied Mathem. & Optimiz., 10: 275-286. Zbl0526.35049MR722491DOI10.1007/BF01448390
  5. LASIECKA, I. and TRIGGIANI, R., 1989. Trace regularity of the solutions of the wave equations with homogeneous Neumann boundary conditions. J.M.A.A., 141: 49-71. Zbl0686.35029MR1004583DOI10.1016/0022-247X(89)90205-9
  6. LASIECKA, I., LIONS, J.L. and TRIGGIANI, R., 1986. Nonhomogeneous boundary value problems for second order hyperbolic operators. J. de Mathématiques Pures et Appliquées, 65: 149-192. Zbl0631.35051MR867669
  7. MIYATAKE, S., 1973. Mixed problems for hyperbolic equations of second order. J. Math. Kyoto University, 13: 435-487. Zbl0281.35052MR333467
  8. SAKAMOTO, R., 1970. Mixed problems for hyperbolic equations. I, II. J. Math. Kyoto University, 10-2: 343-373 and 10-3: 403-417. Zbl0206.40101MR283401
  9. SYMES, W.W., 1983. A trace theorem for solutions of the wave equation and the remote determination of acoustic sources. Mathematical Methods in the Applied Sciences, 5: 131-152. Zbl0528.35085MR703950DOI10.1002/mma.1670050110
  10. TRIGGIANI, R., 1978. A cosine operator approach to modeling L 2 , T ; L 2 ⁢ ( Γ ) -boundary input problems for hyperbolic systems. In «Proceedings 8th IFIP Conference on Optimization Techniques, University of Würzburg, West Germany 1977», Springer-Verlag, Lecture Notes CIS M6: 380-390. Zbl0382.93024MR502082
  11. LASIECKA, I. and TRIGGIANI, R., 1988. A lifting theorem for the time regularity of solutions to abstract equations with unbounded operators and applications to hyperbolic equations. Proceedings Americ. Mathem. Soc., 104: 745-755. Zbl0699.47034MR964851DOI10.2307/2046785
  12. LASIECKA, I. and TRIGGIANI, R., Sharp regularity theory for second order hyperbolic equations of Neumann type. Part I: L 2 non-homodeneous data. Annali di Matematica Pura e Applicata, to appear. Zbl0742.35015MR1142447
  13. LASIECKA, I. and TRIGGIANI, R., 1989. Regularity theory of hyperbolic equations with non-homogeneous Neumann boundary conditions. Part II: General boundary data. J. Differ. Eqts., to appear. Zbl0776.35030

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