"The book is an introduction to advanced analysis at the beginning graduate level that blends a modern presentation with concrete examples and applications, in particular in the areas of calculus of variations and partial differential equations. The book does not strive for abstraction for its own sake, but tries rather to impart a working knowledge of the key methods of contemporary analysis, in particular those that are also relevant for application in physics. It provides a streamlined and quick introduction to the fundamental concepts of Banach space and Lebesgue integration theory and the basic notions of the calculus of variations, including Sobolev space theory."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved
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Limits and Continuity of Functions
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already apply assertion assume assumption Banach space bounded called Cauchy sequence choose closed compact complete compute concept condition consider constant contains continuous functions continuously differentiable converges converges uniformly corollary cube curve defined Definition depends derivative determined differentiable differential equations equicontinuous equivalent everywhere example Exercises exists f is continuous finite fixed follows function f Furthermore given gives harmonic hence holds implies In)neN inequality integrable interval lemma length Let f limit linear lower semicontinuous matrix maximum mean value theorem means measurable metric space namely neighborhood norm obtain operator partial particular pointwise positive precisely problem Proof prove Rd Rd Remark respectively result rule satisfies sequence side solution subsequence subset theorem Theory unique vector space weak