By Olivier Druet,Emmanuel Hebey,Frédéric Robert

ISBN-10: 0691119538

ISBN-13: 9780691119533

Elliptic equations of severe Sobolev progress were the objective of research for many years simply because they've got proved to be of serious value in research, geometry, and physics. The equations studied listed here are of the well known Yamabe style. They contain Schrödinger operators at the left hand aspect and a severe nonlinearity at the correct hand side.

an important improvement within the learn of such equations happened within the Eighties. It used to be came upon that the series splits right into a answer of the restrict equation--a finite sum of bubbles--and a leisure that converges strongly to 0 within the Sobolev area inclusive of sq. integrable features whose gradient can be sq. integrable. This splitting is named the necessary thought for blow-up. during this booklet, the authors enhance the pointwise thought for blow-up. They introduce new rules and strategies that result in sharp pointwise estimates. those estimates have vital functions while facing sharp consistent difficulties (a case the place the strength is minimum) and compactness effects (a case the place the power is arbitrarily large). The authors conscientiously and punctiliously describe pointwise habit whilst the power is arbitrary.

meant to be as self-contained as attainable, this obtainable publication will curiosity graduate scholars and researchers in a number mathematical fields.

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Blow-up Theory for Elliptic PDEs in Riemannian Geometry (MN-45) (Mathematical Notes) by Olivier Druet,Emmanuel Hebey,Frédéric Robert

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