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 significant value in research, geometry, and physics. The equations studied listed here are of the well known Yamabe variety. They contain Schrödinger operators at the left hand facet and a serious nonlinearity at the correct hand side.
an important improvement within the learn of such equations happened within the Eighties. It was once found 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 area including sq. integrable capabilities whose gradient is usually sq. integrable. This splitting is called the quintessential conception for blow-up. during this publication, the authors enhance the pointwise idea for blow-up. They introduce new rules and techniques that bring about sharp pointwise estimates. those estimates have vital purposes whilst facing sharp consistent difficulties (a case the place the power is minimum) and compactness effects (a case the place the power is arbitrarily large). The authors rigorously and punctiliously describe pointwise habit whilst the strength is arbitrary.
meant to be as self-contained as attainable, this obtainable e-book will curiosity graduate scholars and researchers in a variety of mathematical fields.
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Extra info for Blow-up Theory for Elliptic PDEs in Riemannian Geometry (MN-45) (Mathematical Notes)
Blow-up Theory for Elliptic PDEs in Riemannian Geometry (MN-45) (Mathematical Notes) by Olivier Druet,Emmanuel Hebey,Frédéric Robert