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Sobre el curso:
Ésta es la página del Curso Avanzado de Ecuaciones Diferenciales Parciales: Métodos de Espacios de Hilbert. Aquí encontrarás temario, bibliografía, calendario y cualquier material adicional, así como las tareas y anuncios relacionados con el curso.
Contenido:
- Temario del curso, calendario y bibliografía [PDF]
Tareas:
- Tarea 1 [PDF]. Fecha de entrega: pasada.
- Tarea 2 [PDF]. Fecha de entrega: pasada.
- Tarea 3 [PDF]. Fecha de entrega: pasada.
Bibliografía
Bibliografía básica:
- L. C. Evans, Partial Differential Equations, vol. 19 of Graduate Studies in Mathematics, Amer. Math. Soc., Providence, RI, 1998.
- S. Salsa, Partial differential equations in action. From modelling to theory, Universitext, Springer-Verlag, Milan, Italia, 2008.
Bibliografía complementaria:
Teoría de distribuciones
- G. Eskin, Lectures on linear partial differential equations, vol. 123 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI (2011)
- L. Schwartz, Mathematics for the Physical Sciences, Addison-Wesley (1966)
- R. S. Strichartz, A Guide to Distribution Theory and Fourier Transforms, Studies in Advanced Mathematics, CRC-Press, Boca Ratón, Florida (1994)
- A. H. Zemanian, Distribution theory and transform analysis: an introduction to generalized functions, with applications, Dover Publications (1965).
Espacios de Sobolev
- R. A. Adams, Sobolev spaces, Academic Press (1975)
- H. Brezis, Functional Analysis, Sobolev spaces, and Partial Differential Equations, Universitext Springer Verlag (2011)
Ecuaciones elípticas:
- R. Courant, D. Hilbert, Methods of mathematical physics. Vol. II: Partial differential equations. Wiley Classics Library, John Wiley and Sons Inc., New York (1962)
- G. B. Folland, Introduction to Partial Differential Equations, second ed., Princeton University Press (1995)
- D. Gilbarg, N. S. Trudinger, Elliptic partial differential equations of second order, Classics in Mathematics, Springer-Verlag, Berlin (1998)
- Q. Han, F. Lin, Elliptic partial differential equations, vol. 1 of Courant Lecture Notes in Mathematics, New York University Courant Institute of Mathematical Sciences, New York (1997)
- R. E. Showalter, Hilbert space methods in partial differential equations, Electronic Journal of Differential Equations, Monograph no. 1 (1994)
Ecuaciones parabólicas
- O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Uralceva, Linear and quasilinear equations of parabolic type, Translations of Mathematical Monographs vol. 23, American Mathematical Society (1968)
- G. M. Lieberman, Second order parabolic partial differential equations, World Scientific (1996)
- A. Friedman, Partial differential equations of parabolic type, Prentice Hall (1964)
- A. Pazy, Semigroups of linear operators and applications to partial differential equations, Springer verlag (1983)
- M. Renardy, R. C. Rogers, An introduction to partial differential equations, second ed., vol. 13 of Texts in Applied Mathematics, Springer-Verlag, New York (2004)
Ecuaciones hiperbólicas
- S. Alinhac, Hyperbolic partial differential equations, Universitext, Springer Verlag (2009)
- S. Benzoni-Gavage, D. Serre, Multidimensional hyperbolic partial differential equations, first order systems and applications, Oxford University Press (2007)
- O. A. Ladyzhenskaya, The boundary value problems of mathematical physics, vol. 49 of Applied Mathematical Sciences, Springer Verlag (1985)