# [Topics in Analysis] Final Report

Edited by Leun Kim

This report consists of two sections. In the first section, we will prove the global regularity of elliptic partial differential equations. In particular we will extend a result in Hess and Kato [2] to the $L^p$ analogue by applying the theory of pseudo differential operators. In the second section, we will give solutions to some selected exercises which were given in the class.

Sunagawa_Report_20130204_XeTeXFn

References.

[1] M. W. Wong. An Introduction to Pseudo Differential Operators, 2nd edition. World Scientific, pp.127-130, 1999.
[2] P. Hess and T. Kato. Perturbation of Closed Operators and their Adjoints. Comment. Math. Helv, Vol.45, p.527, 1970.
[3] 新井仁之.「新フーリエ解析と関数解析学」 培風館, 2010.
[4] 垣田高夫.「シュワルツ超関数入門」 日本評論社, 1985.
[5] 新開謙三.「擬微分作用素」 裳華房, 1994.
[6] 熊ノ郷準.「擬微分作用素」 岩波書店, 1974.

#### Leun Kim

Ph.D Candidate at The University of Tokyo
I was born and raised in Daegu, S. Korea. I majored in electronics and math in Seoul from 2007 to 2012. I've had a great interest in math since freshman year, and I studied PDE in Osaka, Japan from 2012-2014. I worked at a science museum and HUFS from 2014 in Seoul. Now I'm studying PDE in Tokyo, Japan. I also developed an interest in music, as I met a great piano teacher Oh in 2001, and joined an indie metal band in 2008. In my spare time, I enjoy various things, such as listening music, blogging, traveling, taking photos, and playing Go and Holdem. Please do not hesitate to contact me with comments, email, guestbook, and social medias.