Regularity of perturbed variable exponent double phase functionals

Key Points

• Minimizers for perturbed variable exponent double phase functionals are locally Hölder continuous.
• The study shows that these minimizers are also locally bounded, providing key insights.
• The approach utilizes the De Giorgi iteration to establish regularity in these functionals.
• Understanding the regularity of local minimizers can inform future applications and theories in calculus of variations.