The Dirichlet Energy Integral on Intervals in Variable Exponent Sobolev Spaces | Zendy

Petteri Harjulehto | Zendy; Peter Hästö | Zendy; Mika Koskenoja | Zendy

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The Dirichlet Energy Integral on Intervals in Variable Exponent Sobolev Spaces

Author(s) -

Petteri Harjulehto,

Peter Hästö,

Mika Koskenoja

Publication year - 2003

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1179

Subject(s) - mathematics , sobolev space , lipschitz continuity , exponent , mathematical analysis , dirichlet integral , simple (philosophy) , variable (mathematics) , regular polygon , pure mathematics , real line , space (punctuation) , dirichlet distribution , dirichlet problem , dirichlet's energy , geometry , philosophy , linguistics , boundary value problem , epistemology

In this article we consider Dirichlet energy integral minimizers in variable exponent Sobolev spaces defined on intervals of the real line. We illustrate by examples that the minimizing question is interesting even in this case that is trivial in the classical fixed exponent space. We give an explicit formula for the minimizer, and some simple conditions for when it is convex, concave or Lipschitz continuous. The most surprising conclusion is that there does not exist a minimizer even for every smooth exponent.

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