Positive solution of extremal Pucci’s equations with singular and sublinear nonlinearity

In this paper, we establish the existence of a positive solution to {−M+λ,Λ(D2u)=μk(x)f(u)uα−ηh(x)uqu=0in Ωon ∂Ω, {−Mλ,Λ+(D2u)=μk(x)f(u)uα−ηh(x)uqin Ωu=0on ∂Ω, where ΩΩ is a smooth bounded domain in Rn, n≥1.Rn, n≥1. Under certain conditions on k,f and h,k,f and h, using viscosity sub- and super solution method with the aid of comparison principle, we establish the existence of a unique positive viscosity solution. This work extends and complements the earlier works on semilinear and singular elliptic equations with sublinear nonlinearity.by Jagmohan Tyagi and Ram Baran Verm

Comparison principles and Lipschitz regularity for some nonlinear degenerate elliptic equations

We establish interior Lipschitz regularity for continuous viscosity solutions of fully nonlinear, conformally invariant, degenerate elliptic equations. As a by-product of our method, we also prove a weak form of the strong comparison principle, which we refer to as the principle of propagation of touching points, for operators of the form ∇2ψ + L(x, ψ, ∇ψ) which are non-decreasing in ψ