Strichartz estimates for Maxwell equations in media: the partially anisotropic case

References

• Feynman, R. P., Leighton, R. B., Sands, M. (1964). The Feynman lectures on physics. Vol. 2: mainly electromagnetism and matter. Reading, MA.-London: Addison-Wesley Publishing Co., Inc.
   Google Scholar
• Landau, L. D., Lifschitz, E. M. (1990). Lehrbuch der theoretischen Physik (“Landau-Lifschitz”). Band VIII, 5th ed. Berlin: Akademie-Verlag.
   Google Scholar
• Schippa, R., Schnaubelt, R. (2022). On quasilinear Maxwell equations in two dimensions. Pure Appl. Anal. 4(2):313–365. DOI: 10.2140/paa.2022.4.313.
   Google Scholar
• Moloney, J., Newell, A. (2004). Nonlinear Optics. Advanced Book Program. Boulder, CO: Westview Press.
   Google Scholar
• Lucente, S., Ziliotti, G. (2000). Global existence for a quasilinear Maxwell system. In: Workshop on Blow-up and Global Existence of Solutions for Parabolic and Hyperbolic Problems (Trieste, 1999), Vol. 31, pp. 169–187.
   Google Scholar
• Liess, O. (1991). Decay estimates for the solutions of the system of crystal optics. Asymptotic Anal. 4(1):61–95. DOI: 10.3233/ASY-1991-4103.
   Google Scholar
• Schippa, R. (2022). Resolvent estimates for time-harmonic Maxwell’s equations in the partially anisotropic case. J. Fourier Anal. Appl. 28(2):Paper No. 16, 31.
   Web of Science ®Google Scholar
• Mandel, R., Schippa, R. (2022). Time-harmonic solutions for Maxwell’s equations in anisotropic media and Bochner-Riesz estimates with negative index for non-elliptic surfaces. Ann. Henri Poincaré 23(5):1831–1882. DOI: 10.1007/s00023-021-01144-y.
   Web of Science ®Google Scholar
• Schippa, R., Schnaubelt, R. (2022). Strichartz estimates for Maxwell equations in media: the fully anisotropic case. J. Hyperbolic Differ. Equ. 20(4):917–966. DOI: 10.1142/S0219891623500285.
   Google Scholar
• Dumas, E., Sueur, F. (2012). Cauchy problem and quasi-stationary limit for the Maxwell-Landau-Lifschitz and Maxwell-Bloch equations. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 11(3):503–543.
   Google Scholar
• Darboux, G. (1993). Leçons sur la théorie générale des surfaces. III, IV. Les Grands Classiques Gauthier-Villars. [Gauthier-Villars Great Classics]. Sceaux: Éditions Jacques Gabay.
   Google Scholar
• Keel, M., Tao, T. (1998). Endpoint Strichartz estimates. Amer. J. Math. 120(5):955–980. DOI: 10.1353/ajm.1998.0039.
   Web of Science ®Google Scholar
• Smith, H. F. (1998). A parametrix construction for wave equations with C1,1 coefficients. Ann. Inst. Fourier (Grenoble), 48(3):797–835.
   Web of Science ®Google Scholar
• Tataru, D. (2000). Strichartz estimates for operators with nonsmooth coefficients and the nonlinear wave equation. Amer. J. Math. 122(2):349–376. DOI: 10.1353/ajm.2000.0014.
   Web of Science ®Google Scholar
• Tataru, D. (2001). Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients. II. Amer. J. Math. 123(3):385–423. DOI: 10.1353/ajm.2001.0021.
   Web of Science ®Google Scholar
• Tataru, D. (2002). Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients. III. J. Amer. Math. Soc. 15(2):419–442. DOI: 10.1090/S0894-0347-01-00375-7.
   Web of Science ®Google Scholar
• Bahouri, H., Chemin, J.-V. (1999). Équations d’ondes quasilinéaires et estimations de Strichartz. Amer. J. Math. 121(6):1337–1377. DOI: 10.1353/ajm.1999.0038.
   Web of Science ®Google Scholar
• Klainerman, S. (2001). A commuting vectorfields approach to Strichartz-type inequalities and applications to quasi-linear wave equations. Int. Math. Res. Notices 5:221–274.
   Google Scholar
• Smith, H. F., Tataru, D. (2005). Sharp local well-posedness results for the nonlinear wave equation. Ann. Math. (2) 162(1):291–366. DOI: 10.4007/annals.2005.162.291.
   Web of Science ®Google Scholar
• Taylor, M. E. (1991). Pseudodifferential Operators and Nonlinear PDE, volume 100 of Progress in Mathematics. Boston: Birkhäuser.
   Google Scholar
• Ifrim, M., Tataru, D. (2023). Local well-posedness for quasi-linear problems: a primer. Bull. Amer. Math. Soc. (N.S.) 60(2):167–194. DOI: 10.1090/bull/1775.
   Google Scholar
• Spitz, M. (2017). Local wellposedness of nonlinear Maxwell equations. PhD thesis, Karlsruhe Institute of Technology (KIT).
   Google Scholar
• Spitz, M. (2019). Local wellposedness of nonlinear Maxwell equations with perfectly conducting boundary conditions. J. Differ. Equ. 266(8):5012–5063. DOI: 10.1016/j.jde.2018.10.019.
   Web of Science ®Google Scholar
• Hörmander, L. (2007). The Analysis of Linear Partial Differential Operators. III. Classics in Mathematics. Berlin: Springer. Pseudo-Differential Operators, Reprint of the 1994 edition.
   Google Scholar
• Taylor, M. E. (1981). Pseudodifferential Operators. Princeton Mathematical Series, No. 34. Princeton, NJ: Princeton University Press.
   Google Scholar
• Calderón, A. P., Vaillancourt, R. (1972). A class of bounded pseudo-differential operators. Proc. Nat. Acad. Sci. USA. 69:1185–1187. DOI: 10.1073/pnas.69.5.1185.
   PubMed Web of Science ®Google Scholar
• Delort, J.-M. (1992). F.B.I. Transformation, volume 1522 of Lecture Notes in Mathematics. Berlin: Springer-Verlag.
   Google Scholar
• Hwang, I. L. (1987). The L2-boundedness of pseudodifferential operators. Trans. Amer. Math. Soc. 302(1):55–76.
   Web of Science ®Google Scholar