The eigenvalues and eigenfunctions of the non-linear equation associated to second order Sobolev embeddings
2023
Abstract
We consider the non-linear eigenvalue equations characterizing Lp into Lq Sobolev embeddings of second order for Navier boundary conditions at both ends of a line segment. We give a complete description of the s-numb ers and the extremal functions in the general case (p, q) is an element of (1, infinity)2.
Among other results, we show that these can be expressed in terms of those of related first order embeddings, if and only if p1 + q1 = 1. Our findings shed new light on the surprising nature of higher order Sobolev spaces in the Banach space setting.Crown Copyright (c) 2023 Published by Elsevier Ltd.
This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).