Sobolev Space and L² - Theory of Elliptic Equations

Das, Bidesh (2019) Sobolev Space and L² - Theory of Elliptic Equations. Masters thesis, Indian Institute of Science Education and Research Kolkata.

PDF (MS dissertation of Bidesh Das (14MS166)) 14MS166.pdf - Submitted Version Restricted to Repository staff only Download (990kB)

Abstract

My research works divided into two parts. One part describes basics of Sobolev space. In sobolev part we describes definition of sobolev space, properties of sobolev space, smooth approximation of sobolev function, extension of sobolev function, embedding and compact embedding of sobolev space, Poincar´e Inequality, traces of sobolev functions. In the second parts it describes definition of weak solution of linear elliptic equations, bilinear form, existance and uniqueness of weak solutions by Lax-Milgram’s Theroem, Riesz’s Representation Theroem and Fredholm Alternative Theorem, three kind of regularity of weak solutions and at the end local boudedness of weak solutions by Moser iteration and The De Giorgi-Nash-Moser Theorem.

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