A global Holmgren theorem for multidimensional hyperbolic partial differential equations

References

• Hörmander , L . 1963 . “ Linear Partial Differential Operators ” . In Die Grundlehren Der Mathematischen Wissenschaften, Bd. 116. , New York : Academic Press Inc., Publishers .
   Google Scholar
• Hile , GN and Protter , MH . 1976 . Unique continuation and the cauchy problem for first order systems of partial differential equations . Comm. Partial Diff. Eqns , 1 ( 5 ) : 437 – 465 .
   Google Scholar
• Tataru , D . 1995 . Unique continuation for solutions to PDE's; between Hörmander's theorem and Holmgren's theorem . Comm. Partial Diff. Eqns , 20 ( 5--6 ) : 855 – 884 .
   Google Scholar
• Tataru , D . 1999 . Unique continuation for operators with partially analytic coefficients . J. Math. Pures Appl. (9) , 78 ( 5 ) : 505 – 521 .
   Web of Science ®Google Scholar
• Eller , M , Isakov , V , Nakamura , G and Tataru , D . 2002 . “ Uniqueness and stability in the cauchy problem for maxwell and elasticity systems ” . In in Nonlinear partial differential equations and their applications. Collège de France Seminar, Vol. XIV (Paris, 1997/1998), Studies in Applied Mathematics , Vol. 31 , 329 – 349 . Amsterdam : North-Holland .
   Google Scholar
• John , F . 1949 . On linear partial differential equations with analytic coefficients. Unique continuation of data . Comm. Pure Appl. Math. , 2 : 209 – 253 .
   Google Scholar
• Isakov , V . 2006 . Inverse Problems for Partial Differential Equations, , 2 , Berlin : Springer-Verlag .
   Google Scholar
• Littman , W . 2000 . “ Remarks on Global Uniqueness Theorems for Partial Differential Equations ” . In in Differential Geometric Methods in the Control of Partial Differential Equations (Boulder, CO, 1999), Contemporary Mathematics , Vol. 268 , 363 – 371 . Providence, RI : American Mathematical Society .
   Google Scholar
• Conway , JB . 1990 . “ A Course in Functional Analysis ” . In Graduate Texts in Mathematics, , 2 , Vol. 96 , New York : Springer-Verlag .
   Google Scholar
• Bao , D , Chern , S-S and Shen , Z . 2000 . An Introduction to Riemann-Finsler Geometry, Graduate Texts in Mathematics , Vol. 200 , New York : Springer-Verlag .
   Google Scholar
• Courant , R and Hilbert , D . 1962 . “ Methods of Mathematical Physics ” . In Vol. II: Partial Differential Equations. (Vol. II by R. Courant.) , New York-London : Interscience Publishers (a division of John Wiley & Sons) .
   Google Scholar
• Duff , GFD . 1960 . The Cauchy problem for elastic waves in an anisotropic medium . Philos. Trans. Roy. Soc. London Ser. A , 252 : 249 – 273 .
   Google Scholar
• Kline , M and Kay , IW . 1965 . “ Electromagnetic Theory and Geometrical Optics ” . In Pure and Applied Mathematics , Vol. XII , New York-London-Sydney : Interscience Publishers, John Wiley & Sons, Inc. .
   Google Scholar
• Reissner , E . 1945 . The effect of transverse shear deformation on the bending of elastic plates . J. Appl. Mech. , 12 : A – 69--A--77 .
   Google Scholar
• Mindlin , RD . 1951 . Thickness-shear and exural vibrations of crystal plates . J. Appl. Phys. , 22 : 316 – 323 .
   Google Scholar
• Rayleigh , JWilliam and Strutt , B . 1945 . The Theory of Sound, , 2d , New York : Dover Publications .
   Google Scholar
• Timoshenko , SP . 1953 . The Collected Papers of Stephen P. Timoshenko , New York-Toronto-London : McGraw-Hill Book Company, Inc. .
   Google Scholar
• Lagnese , JE . 1989 . “ Boundary Stabilization of Thin Plates ” . In SiAM Studies in Applied Mathematics , Vol. 10 , Philadelphia, PA : Society for Industrial and Applied Mathematics (SIAM) .
   Google Scholar
• Fedorov , FI . 1963 . Theory of Elastic Waves in Crystals , New York : Plenum Press .
   Google Scholar
• Payton , RG . 1983 . “ Elastic Wave Propagation in Transversely Isotropic Media ” . In Mechanics of Elastic and Inelastic Solids 4 , The Hague : Martinus Nijhoff Publishers .
   Google Scholar
• Mazzucato , AL and Rachele , LV . 2008 . On transversely isotropic elastic media with ellipsoidal slowness surfaces . Math. Mech. Solids , 13 ( 7 ) : 611 – 638 .
   Google Scholar
• Eller , MM . 2003 . Unique continuation for solutions to Maxwell's system with non-analytic anisotropic coefficients . J. Math. Anal. Appl. , 284 ( 2 ) : 698 – 710 .
   Google Scholar