The Interplay between Analysis and Topology in Some Nonlinear Pde Problems
نویسنده
چکیده
The “balayage” method introduced by H. Poincaré in his proof of Theorem 1 relies heavily on tools of Potential theory: maximum principle, Harnack’s inequality, explicit representation formulas for the Dirichlet problem in a ball (Poisson integral), etc. In 1900, D. Hilbert [39], in a celebrated address, followed by a (slightly) more detailed paper in 1904, announced that he had solved the Dirichlet problem (0.1) (0.2) via the Dirichlet principle which had been discovered by G. Green in 1833, with later contributions by C. F. Gauss (1837), W. Thomson (=Lord Kelvin) (1847) and G. Riemann (1853). Dirichlet’s principle asserts that any solution u of (0.1) (0.2) is a minimizer of the Dirichlet integral
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