On the minimisation of the peak–to–average ratio
Year: 2025
Type: article
Abstract: Let $$\Omega \Subset \mathbb R^n$$ Ω ⋐ R n and a continuous function $$\textrm{H}: \Omega \times \mathbb R^N \times \mathbb R^{N n} \times \cdots \times \mathbb R^{N n^{k}}_s \longrightarrow \mathbb R$$ H : Ω × R N × R Nn × ⋯ × R s N n k ⟶ R be given, where $$n,k,N \in \mathbb N$$ n , k , N ∈ N . For $$p\in [1,\infty ]$$ p ∈ [ 1 , ∞ ] , we consider the functional $$\begin{aligned} \ \ \ \ \ \mathrm E_p(u) := \big \Vert \mathrm H \big (\cdot ,u,\mathrm D u, \ldots , \mathrm D^ku \big ) \big \Vert _{\mathrm L^p(\Omega )},\ \ \ u\in \mathrm W^{k,p}(\Omega ;\mathbb R^N). \end{aligned}$$ E p ( u ) : = ‖ H ( · , u , D u , … , D k u ) ‖ L p ( Ω ) , u ∈ W k , p ( Ω ; R N ) . In this note we are interested in the $$\textrm{L}^\infty $$
Author: Nikos Katzourakis
Institution: University of Reading
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4415586317