Regularity of solutions to a class of variable–exponent fully nonlinear elliptic equations

Regularity for solutions of fully nonlinear elliptic equations with nonhomogeneous degeneracy

“…Several aspects of this class of partial differential equations have already been investigated: comparison principle and Liouville-type theorems [7], properties of eigenvalues and eigenfunctions [8,9], Alexandrov-Bakelman-Pucci estimates [20,29], Harnack inequalities [21,29] and regularity [10,11,30]. In particular, in order to study possible anisotropic problems, in [12] the variable exponent case for the degeneracy is analysed: precisely, it is shown that viscosity solutions of equations modelled on…”

A degenerate fully nonlinear free transmission problem with variable exponents

“…with β + and β − corresponding to the positive and negative parts of β, respectively. The estimates obtained in [7] are independent of the continuity modulus of β.…”

“…The methods introduced in [12] resonated, launching new perspectives in the theory of degenerate fully nonlinear equations. In [7], the authors consider the equation…”

Hölder gradient regularity for the inhomogeneous normalized $p(x)$-Laplace equation

“…For other related results, see for example the works of Attouchi, Parviainen and Ruosteenoja [APR17] on the normalized p-Poisson problem −∆ N p u = f , Attouchi and Ruosteenoja [AR18, AR20, Att20] on the equation − |Du| γ ∆ N p u = f and its parabolic version, De Filippis [DF21] on the double phase problem (|Du| q + a(x) |Du| s )F (D 2 u) = f (x) and Fang and Zhang [FZ21b] on the parabolic double phase problem ∂ t u = (|Du| q + a(x, t) |Du| s )∆ N p u. We also mention the paper by Bronzi, Pimentel, Rampasso and Teixeira [BPRT20] where they consider fully nonlinear variable exponent equations of the type |Du| θ(x) F (D 2 u) = 0.…”