This book serves as a bridge between graduate textbooks and research articles in the area of nonlinear elliptic partial differential equations. Whereas graduate textbooks present basic concepts, the student can hardly get a feel for research by relying solely on such texts; by contrast, whereas journal articles present results on the forefront of research, such texts offer little, if anything, in ...
Series: Aims Series on Differential Equations & Dynamical Systems (Book 4)
Hardcover: 299 pages
Publisher: American Institute of Mathematical Sciences; 1st edition (July 29, 2010)
Product Dimensions: 6.2 x 0.8 x 9.2 inches
Amazon Rank: 748502
Format: PDF ePub fb2 djvu ebook
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requisite background material. If this dilemma sounds all too familiar, and you would like to commence hands-on research immediately, this is the book for you; for the purpose of this text is to prepare both graduate students and young mathematicians to readily engage in research and to solve related problems. This volume is self-contained in that it provides both background material and typical methods used in nonlinear analysis, such as: 1) Sobolev Spaces on Euclidean spaces and Riemannian manifolds; 2) Variational methods and critical point theory; 3) Equations on prescribing Gaussian and scalar curvature; 4) Regularity of solutions; 5) Various maximum principles and methods of moving planes. Moreover, it presents new ideas from the research front, including: 1) Regularity lifting by the combined use of contracting and shrinking operators; 2) The method of moving planes in integral forms.