Using Functional Analysis and Sobolev Spaces to Solve Poisson’s Equation
نویسنده
چکیده
We study Banach and Hilbert spaces with an eye towards defining weak solutions to elliptic PDE. Using Lax-Milgram we prove that weak solutions to Poisson’s equation exist under certain conditions.
منابع مشابه
Functional Anaysis for Engineers
4 Sobolev-Spaces 23 4.1 Basic Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.2 Poisson’s Problem . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.3 Abstract Eigenvalue Problem . . . . . . . . . . . . . . . . . . 30 4.4 Sobolev Spaces for Periodic Functions . . . . . . . . . . . . . . 32 4.5 Fractional Sobolev Spaces for Periodic Functions . . . . . . . . 32 4.6 Trace T...
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تاریخ انتشار 2016