In this paper, we consider L∞ estimates of eigenfunction, or more generally,
the L∞ estimates of equation
-Δu=fu. We use heat flow to give a new proof of the L∞ estimates for such type equations.
References
[1]
Evans, L.C. (1998) Partial Differential Equations, Graduate Studies in Mathematics, 19. American Mathematical Society, Providence.
[2]
Gilbarg, D. and Trudinger, N.S. (2001) Elliptic Partial Differential Equations of Second Order. Reprint of the 1998 Edition, Springer-Verlag, Berlin.
[3]
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.
[4]
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
[5]
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
