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Fundamental properties of solutions of a degenerate elliptic equation in extended space

โœ Scribed by Xinhua Ji; Dequan Chen

Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
769 KB
Volume
58
Category
Article
ISSN
0022-0396

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๐Ÿ“œ SIMILAR VOLUMES

Properties of Poisson kernel for a degen
Properties of Poisson kernel for a degenerate elliptic equation
โœ Xinhua Ji; Tao Qian ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 105 KB ๐Ÿ‘ 2 views

In this note we prove that the Poisson kernel given in [5] satis"es the basic properties of the usual Poisson kernel. We further obtain solutions of the associated Dirichlet problem with C(SL\)-boundary value functions for the degenerate elliptic equation extending the work in [4}6].

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We prove the existence of bounded solutions of some boundary value problems for degenerate elliptic equations of second order in divergence form. Our results cover also the unbounded domain case. We discuss also the uniqueness problem and asymptotic behaviour of the solutions of our equation.