On an application of hypoellipticity to solutions of functional equations |
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Authors: | Akira Tsutsumi Shigeru Haruki |
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Affiliation: | (1) Department of Applied Mathematics, Osaka Women's University, 590 Sakai, Osaka, Japan;(2) Department of Applied Mathematics, Graduate School, Okayama University of Science, 700 Ridai-cho, Okayama, Japan |
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Abstract: | Summary We study the regularity of solutions of functional equations of a generalized mean value type. In this paper we give sufficient conditions for the regularity by using hypoellipticity which is a concept of the theory of partial differential equations. We also give an affirmative answer to a conjecture of H. wiatak. A part of the results was announced in the comprehensive paper [8] on our joint works. To prove the regularity of solutions of functional equations is one of the central problems in the theory of functional equations (see [1]). |
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Keywords: | Primary 39B20, 39B30 Secondary 35H05, 35H65 |
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