Search results for "Nirenberg and Matthaei experiment"

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Symmetry for positive critical points of Caffarelli–Kohn–Nirenberg inequalities

2022

Abstract We consider positive critical points of Caffarelli–Kohn–Nirenberg inequalities and prove a Liouville type result which allows us to give a complete classification of the solutions in a certain range of parameters, providing a symmetry result for positive solutions. The governing operator is a weighted p -Laplace operator, which we consider for a general p ∈ ( 1 , d ) . For p = 2 , the symmetry breaking region for extremals of Caffarelli–Kohn–Nirenberg inequalities was completely characterized in Dolbeault et al. (2016). Our results extend this result to a general p and are optimal in some cases.

Pure mathematicsApplied MathematicsOperator (physics)Caffarelli–Kohn–Nirenberg inequalities Classification of solutions Liouville-type theorem Optimal constant Quasilinear anisotropic elliptic equationsMathematics::Analysis of PDEsType (model theory)Range (mathematics)Settore MAT/05 - Analisi MatematicaSymmetry breakingSymmetry (geometry)Nirenberg and Matthaei experimentLaplace operatorAnalysisMathematics
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The norm of the characteristic function of a set in the John‐Nirenberg space of exponent p

2020

Set (abstract data type)Characteristic function (convex analysis)Pure mathematicsGeneral MathematicsGeneral EngineeringExponentSpace (mathematics)Nirenberg and Matthaei experimentBounded mean oscillationMathematicsMathematical Methods in the Applied Sciences
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