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A priori bounds for elliptic equations

✍ Scribed by E. Lemus; P. Padilla

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 243 KB
Volume: 30
Category: Article
ISSN: 0362-546X
DOI: 10.1016/s0362-546x(97)00144-2

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✦ Synopsis

In this paper we study the relationship existing between the maximum principle and the principrtl eigcnvalue of second order elliptic operators and the expected exit times of the corresponding diffusions. A probabilistic approach is discussed that provides a good understanding of classical results established analytically. We also obtain an Alexandrov-Bakelman-Pucci type of estimate using similar methods.

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## Abstract In the investigation of the spectral theory of non‐selfadjoint elliptic boundary value problems involving an indefinite weight function, there arises the problem of obtaining __L^p^__ a priori estimates for solutions about points of discontinuity of the weight function. Here we deal wit