Uniform estimates for solutions of nonlinear Klein-Gordon equations

Uniform estimates in $\text{H}{}_0{}^1\text{(Ω)}$ of global solutions to nonlinear Klein-Gordon equations of the form $\text{u}{}_{\mathrm{tt}}\text{? Δu + mu = g(u)}\text{in}\text{Ω, u = 0}\text{in}\text{?Ω}$, where Ω is an open subset of $\text{R}$^N, m > 0, and g satisfies some growth conditions are established.