Schütz, Lineia; Ziebell, Juliana S.; Zingano, Janaína P.; Zingano, Paulo R. Sharp pointwise estimates for functions in the Sobolev spaces \(H^s(\mathbb R^n)\). (English) Zbl 1357.46033 Adv. Differ. Equ. Control Process. 16, No. 1, 45-53 (2015). Summary: We provide the optimal value of the constant \(K(n,m)\) in the Gagliardo-Nirenberg supnorm inequality \[ \|u \|_{L^{\infty}\mathbb R^n} \leq K(n,m) \|u\|^{-1 \frac{2}{2m}}_{L^2(\mathbb R^n)}\|D^m u\|^{\frac{2}{2m}}_{L^2(\mathbb R^n)}, \;m>n/2, \] and its generalizations to the Sobolev spaces \(H^s(\mathbb R^n)\) of arbitrary order \(s>n/2\) as well. Cited in 3 Documents MSC: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 35A23 Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals 26D10 Inequalities involving derivatives and differential and integral operators Keywords:Sobolev embedding property; optimal pointwise inequality; sharp Gagliardo-Nirenberg inequality; optimal Sobolev inequality; optimal constant PDFBibTeX XMLCite \textit{L. Schütz} et al., Adv. Differ. Equ. Control Process. 16, No. 1, 45--53 (2015; Zbl 1357.46033) Full Text: DOI arXiv Link