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Proof of two conjectures of H. Brezis and L.A. Peletier

✍ Scribed by Olivier Rey


Book ID
105103256
Publisher
Springer
Year
1989
Tongue
English
Weight
659 KB
Volume
65
Category
Article
ISSN
0025-2611

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We study the existence of minimizing solutions for an elliptic equation involving critical Sobolev exponent on domains of the three-dimensional Euclidean space. We solve in particular by the affirmative a conjecture of HaΓ―m Brezis. The similar situation in higher dimensions was completely understood

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Let \(M_{n}\) be the Minkowski fundamental domain for the space of \(n \times n\) real, symmetric, and positive definite matrices under the action of the unimodular group \(S L_{n}(Z)\). C. L. Siegel conjectured that \(d(A, B)-f(A, B) \leqslant C(n)\), for \(A, B \in M_{n}\), where \(d\) and \(f\) a