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Bezig met laden... Blow-up Theory for Elliptic PDEs in Riemannian Geometrydoor Olivier Druet, Emmanuel Hebey (Auteur), Frédéric Robert (Auteur)
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Onderdeel van de uitgeversreeks(en)Mathematical Notes (45)
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 Schr©œdinger 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. Geen bibliotheekbeschrijvingen gevonden. |
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Google Books — Bezig met laden... GenresDewey Decimale Classificatie (DDC)515.353Natural sciences and mathematics Mathematics Analysis Differential calculus and equations Differental equations Partial differential equationsLC-classificatieWaarderingGemiddelde: Geen beoordelingen.Ben jij dit?Word een LibraryThing Auteur. |