Table of Contents
ISRN Mathematical Analysis
Volume 2011 (2011), Article ID 469795, 14 pages
http://dx.doi.org/10.5402/2011/469795
Research Article

Connecting Classical and Abstract Theory of Friedrichs Systems via Trace Operator

1Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10002 Zagreb, Croatia
2Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, 31000 Osijek, Croatia

Received 4 May 2011; Accepted 5 June 2011

Academic Editors: D. Han and G. Schimperna

Copyright © 2011 Nenad Antonić et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. K. O. Friedrichs, “Symmetric positive linear differential equations,” Communications on Pure and Applied Mathematics, vol. 11, pp. 333–418, 1958. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. N. Antonić and K. Burazin, “Graph spaces of first-order linear partial differential operators,” Mathematical Communications, vol. 14, no. 1, pp. 135–155, 2009. View at Google Scholar · View at Zentralblatt MATH
  3. M. Jensen, Discontinuous Galerkin methods for Friedrichs systems with irregular solutions, Ph.D. thesis, University of Oxford, 2004.
  4. L. Tartar, An Introduction to Sobolev Spaces and Interpolation Spaces, vol. 3 of Lecture Notes of the Unione Matematica Italiana, Springer, Berlin, Germany, 2007.
  5. J. Rauch, “Boundary value problems with nonuniformly characteristic boundary,” Journal de Mathématiques Pures et Appliquées, vol. 73, no. 4, pp. 347–353, 1994. View at Google Scholar · View at Zentralblatt MATH
  6. A. Ern and J.-L. Guermond, “Discontinuous Galerkin methods for Friedrichs' systems,” SIAM Journal on Numerical Analysis, vol. 44, no. 6, pp. 2363–2388, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. A. Ern, J.-L. Guermond, and G. Caplain, “An intrinsic criterion for the bijectivity of Hilbert operators related to Friedrichs' systems,” Communications in Partial Differential Equations, vol. 32, no. 1–3, pp. 317–341, 2007. View at Publisher · View at Google Scholar
  8. N. Antonić and K. Burazin, “Intrinsic boundary conditions for Friedrichs systems,” Communications in Partial Differential Equations, vol. 35, no. 9, pp. 1690–1715, 2010. View at Publisher · View at Google Scholar
  9. N. Antonić and K. Burazin, “On equivalent descriptions of boundary conditions for Friedrichs systems,” to appear in Mathematica Montisnigri. View at Publisher · View at Google Scholar
  10. N. Antonić and K. Burazin, “Boundary operator from matrix field formulation of boundary conditions for Friedrichs systems,” Journal of Differential Equations, vol. 250, no. 9, pp. 3630–3651, 2011. View at Publisher · View at Google Scholar
  11. N. Antonić, K. Burazin, and M. Vrdoljak, “Second-order equations as Friedrichs systems,” Nonlinear Analysis B: Real World Applications. In press. View at Publisher · View at Google Scholar
  12. K. Burazin, Contributions to the theory of Friedrichs' and hyperbolic systems, Ph.D. thesis, University of Zagreb, 2008, http://www.mathos.hr/~kburazin/papers/teza.pdf.