Methods on Nonlinear Elliptic Equations

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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.

Methods on Nonlinear Elliptic Equations

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