The isoperimetric problem for Holderian curves

TL;DR

This paper establishes a necessary condition for solving isoperimetric variational problems involving non-differentiable, H"{o}lder continuous curves using scale derivatives, advancing the calculus of variations for irregular functions.

Contribution

It introduces a stationary condition for isoperimetric problems with non-differentiable curves within the framework of scale derivatives, extending classical variational methods.

Findings

Derived a necessary stationary condition for H"{o}lder continuous curves.

Extended variational calculus to include non-differentiable functions.

Applicable to isoperimetric problems with irregular curves.

Abstract

We prove a necessary stationary condition for non-differentiable isoperimetric variational problems with scale derivatives, defined on the class of H\"{o}lder continuous functions.