Elliptic and Parabolic Equations
نویسنده
چکیده
Elliptic equations: 1. Harmonic functions 2. Perron’s method 3. Potential theory 4. Existence results; the method of suband supersolutions 5. Classical maximum principles for elliptic equations 6. More regularity, Schauder’s theory for general elliptic operators 7. The weak solution approach in one space dimension 8. Eigenfunctions for the Sturm-Liouville problem 9. Generalization to more dimensions Parabolic equations: 10. Maximum principles for parabolic equations 11. Potential theory and existence results 12. Asymptotic behaviour of solutions to the semilinear heat equation Functional Analysis: A. Banach spaces B. Hilbert spaces C. Continous semigroups and Liapounov functionals
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A pseudo - monotonicity adapted to doubly nonlinear elliptic - parabolic equations
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