Research ArticleOpen AccessGoogle Scholar indexed
A Remark on Eigenfunction Estimates by Heat Flow
Department of Mathematics, Beijing Jiaotong University, Beijing, China
College of Engineering, Peking University, Beijing, China
- 1 Department of Mathematics, Beijing Jiaotong University, Beijing, China
- 2 College of Engineering, Peking University, Beijing, China
Advances in Pure Mathematics·Volume 06 (2016)·Pages 512–515·Published 14 June 2016·DOI10.4236/apm.2016.67038
Copy link · social · email
Abstract
In this paper, we consider L ∞ estimates of eigenfunction, or more generally, the L ∞ estimates of equation -Δu= f u. We use heat flow to give a new proof of the L ∞ estimates for such type equations.
Keywords<i>L</i><sup>&infin</sup>EstimatesEigenfunctionHeat Flow
- Evans, L.C. (1998) Partial Differential Equations, Graduate Studies in Mathematics, 19. American Mathematical Society, Providence.
- Gilbarg, D. and Trudinger, N.S. (2001) Elliptic Partial Differential Equations of Second Order. Reprint of the 1998 Edition, Springer-Verlag, Berlin.
- Han, Q. and Lin, F. (2011) Elliptic Partial Differential Equations. 2rd Edition, Courant Lecture Notes in Mathematics, 1. Courant Institute of Mathematical Sciences, American Mathematical Society, New York, Providence.
- Moser, J. (1964) A Harnack Inequality for Parabolic Differential Equations. Communications on Pure and Applied Mathematics, 17, 101-134. http://dx.doi.org/10.1002/cpa.3160170106
- Moser, J. (1961) On Harnack’s Theorem for Elliptic Differential Equations. Communications on Pure and Applied Mathematics, 14, 577-591. http://dx.doi.org/10.1002/cpa.3160140329