Sharp decay estimates for subsolutions of fully nonlinear equations in thin domains

Abstract

We reduce the problem of establishing pointwise upper decay estimates in thin domains for viscosity subsolutions of fully nonlinear partial differential equations to solving a one-dimensional differential inequality. The resulting estimates make explicit the interaction between the transverse geometry of the domain and the ellipticity of the equation, and are shown to be sharp. Our framework allows the ellipticity to degenerate at infinity and accommodates nonhomogeneous equations with lower-order terms. As an application, we obtain decay estimates for $p$-subharmonic functions when $1<p\leq 2$