Regularity of solutions to degenerate fully nonlinear elliptic equations with variable exponent

Abstract

We consider the fully nonlinear equation with variable-exponent double phase type degeneracies $$[|Du{|}^{p(x)}+a(x)|Du{|}^{q(x)}]F(D^{2}u)=f(x).$$ Under some appropriate assumptions, by making use of geometric tangential methods and combing a refined improvement-of-flatness approach with compactness and scaling techniques we obtain the sharp local $C^{1,\alpha }$ regularity of viscosity solutions to such equations.

References in corpus (1)

• Regularity for minimizers for functionals of double phase with variable exponents