By Olivier Druet,Emmanuel Hebey,Frédéric Robert
ISBN-10: 0691119538
ISBN-13: 9780691119533
Elliptic equations of severe Sobolev development 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 sort. They contain Schrödinger operators at the left hand part and a severe nonlinearity at the correct hand side.
an important improvement within the learn of such equations happened within the Nineteen Eighties. It used to be came across that the series splits right into a answer of the restrict equation--a finite sum of bubbles--and a relaxation that converges strongly to 0 within the Sobolev house such as sq. integrable features whose gradient can be sq. integrable. This splitting is called the imperative conception for blow-up. during this booklet, the authors enhance the pointwise idea for blow-up. They introduce new rules and techniques that bring about sharp pointwise estimates. those estimates have very important purposes while facing sharp consistent difficulties (a case the place the strength is minimum) and compactness effects (a case the place the strength 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 ebook will curiosity graduate scholars and researchers in various 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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