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Let $(X,\omega)$ be a compact Hermitian manifold. We establish a stabilityresult for solutions to complex Monge-Amp\`ere equations with right-hand sidein $L^p$, $p>1$. Using this we prove that the solutions are H\"older continuouswith the same exponent as in the K\"ahler case \cite{DDGKPZ14}. Our techniquesalso apply to the setting of big cohomology classes on compact K\"ahlermanifolds.

Stability and H\"older regularity of solutions to complex Monge-Amp\`ere equations on compact Hermitian manifolds