Higher Hölder regularity for fractional (p, q) -Laplace equations

Key Points

• Hölder estimates with explicit exponents were established for fractional (p,q)-Laplace equations, enhancing understanding of regularity.
• The study reveals a Liouville-type theorem, providing significant implications for the uniqueness of solutions across fractional spaces.
• Approaches used involve techniques from the fractional p-Laplace equation, particularly utilizing Moser-type iterations to analyze regularity.
• This groundwork may lead to further advancements in non-linear fractional differential equations and their applications.