Avisos:
» Ya está disponible la Tarea
1. La fecha de entrega se determinarámás
adelante.
Sobre el curso:
El objetivo principal del curso es introducir al estudiante
a la teoría lineal de ecuaciones diferenciales parciales
elípticas basada en espacios de Sobolev. Se discutirán:
espacios de Hilbert y de Banach, teoría de distribuciones,
espacios de Sobolev y ecuaciones lineales de tipo elíptico.
Contenido:
- Calendario 2024-2 (plan semestral): [PDF].
- Temario, calendario y bibliografía del curso [PDF].
- Página del Posgrado en Ciencias Matemáticas.
Material auxiliar:
Próximamente.Tareas:
- Tarea 1 [PDF].
Fecha de entrega: por determinar.
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:
Análisis Funcional
- A. Bressan, Lecture Notes on Functional Analysis, vol. 143 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, 2013.
- S. Kesavan, Topics in functional analysis and applications, John Wiley & Sons, Inc., New York, 1989.
- K. Rektorys, Variational methods in mathematics,
science and engineering, D. Reidel Publishing Co.,
Dordrecht, second ed., 1980.
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.
- G. Eskin, Lectures on Linear Partial Differential
Equations, vol. 123 of Graduate Studies in
Mathematics, American Mathematical Society, Providence, RI,
2011.
- G. Leoni, A First Course in Sobolev spaces, vol.
181 of Graduate Studies in Mathematics, American
Mathematical Society, Providence, RI, second ed., 2017.
Ecuaciones elípticas
- H. Attouch, G. Buttazzo, G. Michaille, Variational
Analysis in Sobolev and BV Spaces, second ed. Society
of Industrial and Applied Mathematics, Philadelphia, PA,
2014.
- 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.