Work

Optimality of embeddings in Orlicz spaces

Year: 2025

Type: article

Abstract: Working with function spaces in various branches of mathematical analysis introduces optimality problems, where the question of choosing a function space both accessible and expressive becomes a nontrivial exercise. A good middle ground is provided by Orlicz spaces, parameterized by a single Young function and thus accessible, yet expansive. In this work, we study optimality problems on Sobolev embeddings in the so‐called Maz'ya classes of Euclidean domains which are defined through their isoperimetric behavior. In particular, we prove the non‐existence of optimal Orlicz spaces in certain Orlicz–Sobolev embeddings in a limiting (critical) state, whose pivotal special case is the celebrated embedding of Brezis and Wainger for John domains.

Source: Mathematische Nachrichten

DOI: 10.1002/mana.12036

Author: Tomáš Beránek

Institution: Charles University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,460

Funder: Grantová Agentura České Republiky