EDP Sem II 2023-2024
Seria 32 (grupe 321, 322) , curs si seminar
In cadrul acestui curs ne vom concentra pe doua teme principale:
1. Metoda directa a calculului variational (MDCV). Aplicatii la rezolvarea EDP eliptice semiliniare (aprox 2 saptamani).
2. Distributii si transformata Fourier. Aplicatii la rezolvarea EDP (aprox 8 saptamani).
Bibliografie (extinsa)
1. H. Brezis: Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011. xiv+599 pp.
2. H. Brezis, L. Nirenberg:Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), no. 4, 437477.
3. B. Dacorogna. Direct methods in the calculus of variations. Second edition. Applied Mathematical Sciences, 78. Springer, New York, 2008. xii+619 pp.
4. L. C. Evans: Partial differential equations, Graduate Studies in Mathematics, 19, Second Edittion, American Mathematical Society, Providence, RI, 2010, xxii+749.
5. F. Linares and G. Ponce: Introduction to nonlinear dispersive equations, Springer, New York, 2009, xii+256 pp.
6. L. Schwartz: Théorie des distributions: (French) Publications de l'Institut de Mathematique de l'Universite de Strasbourg, No. IX-X. Nouvelle edition, entièrement corrigé, refondue et augmentée. Hermann, Paris 1966 xiii+420 pp.
7. E. Stein, R. Shakarchi: Fourier analysis. An introduction. Princeton Lectures in Analysis, Princeton University Press, Princeton, NJ, 2003. xvi+311 pp.
8. L. Ignat, M. Mihailescu, personal communications.