Get Blow-up Theory for Elliptic PDEs in Riemannian Geometry PDF

By Olivier Druet,Emmanuel Hebey,Frédéric Robert

Elliptic equations of severe Sobolev progress were the objective of research for many years simply because they've got proved to be of serious significance 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 facet and a severe nonlinearity at the correct hand side.

an important improvement within the learn of such equations happened within the Eighties. It was once 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 house including sq. integrable services whose gradient is usually sq. integrable. This splitting is called the indispensable concept for blow-up. during this booklet, the authors boost the pointwise conception for blow-up. They introduce new rules and techniques that bring about sharp pointwise estimates. those estimates have vital functions whilst 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 carefully describe pointwise habit while the power is arbitrary.

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

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