On a class of evolution equations in Lipschitz subdomains of Riemannian manifolds

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We study the existence, uniqueness, analyticity, and continuous dependence of mild solutions for a class of evolutionary integrodifferential equations with free boundary conditions on L p -spaces in Lipschitz subdomains of Riemannian manifolds. Our strategy is to use the Laplace transform theory to ensure the existence of an analytic resolvent to the Hodge–Laplacian in the space of all ℓ-differential forms with p-th power integrable coefficients.