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Analytical spaces --- Espaces de Sobolev --- Menigvuldigheden van Riemann --- Riemannian manifolds --- Ruimten van Sobolev --- Sobolev [Espaces de ] --- Sobolev [Ruimten van ] --- Sobolev spaces --- Spaces [Sobolev ] --- Variétés de Riemann --- Sobolev spaces. --- Riemannian manifolds. --- Periodicals

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Sobolev spaces --- Inequalities (Mathematics) --- Riemannian manifolds --- Géometrie de Riemann --- Géometrie de Riemann --- Inégalités variationnelles --- Analyse sur une variété

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Sobolev spaces --- Inequalities (Mathematics) --- Riemannian manifolds --- Sobolev, Espaces de --- Inégalités (Mathématiques) --- Riemann, Variétés de

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Elliptic equations of critical Sobolev growth have been the target of investigation for decades because they have proved to be of great importance in analysis, geometry, and physics. The equations studied here are of the well-known Yamabe type. They involve Schrödinger operators on the left hand side and a critical nonlinearity on the right hand side. A significant development in the study of such equations occurred in the 1980's. It was discovered that the sequence splits into a solution of the limit equation--a finite sum of bubbles--and a rest that converges strongly to zero in the Sobolev space consisting of square integrable functions whose gradient is also square integrable. This splitting is known as the integral theory for blow-up. In this book, the authors develop the pointwise theory for blow-up. They introduce new ideas and methods that lead to sharp pointwise estimates. These estimates have important applications when dealing with sharp constant problems (a case where the energy is minimal) and compactness results (a case where the energy is arbitrarily large). The authors carefully and thoroughly describe pointwise behavior when the energy is arbitrary. Intended to be as self-contained as possible, this accessible book will interest graduate students and researchers in a range of mathematical fields.

Calculus of variations. --- Differential equations, Nonlinear. --- Geometry, Riemannian. --- Riemann geometry --- Riemannian geometry --- Generalized spaces --- Geometry, Non-Euclidean --- Semi-Riemannian geometry --- Nonlinear differential equations --- Nonlinear theories --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Asymptotic analysis. --- Cayley–Hamilton theorem. --- Contradiction. --- Curvature. --- Diffeomorphism. --- Differentiable manifold. --- Equation. --- Estimation. --- Euclidean space. --- Laplace's equation. --- Maximum principle. --- Nonlinear system. --- Polynomial. --- Princeton University Press. --- Result. --- Ricci curvature. --- Riemannian geometry. --- Riemannian manifold. --- Simply connected space. --- Sphere theorem (3-manifolds). --- Stone's theorem. --- Submanifold. --- Subsequence. --- Theorem. --- Three-dimensional space (mathematics). --- Topology. --- Unit sphere.