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Differential equations, Elliptic --- Equations différentielles elliptiques --- Equations différentielles elliptiques

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"In this paper we study elliptic PDEs on compact Gromov-Hausdorff limit spaces of Riemannian manifolds with lower Ricci curvature bounds. In particular we establish continuities of geometric quantities, which include solutions of Poisson's equations, eigenvalues of Schrödinger operators, generalized Yamabe constants and eigenvalues of the Hodge Laplacian, with respect to the Gromov-Hausdorff topology. We apply these to the study of second-order differential calculus on such limit spaces"--

Geometry, Differential. --- Differential equations, Elliptic. --- Géométrie différentielle. --- Équations différentielles elliptiques. --- Geometry, Differential --- Differential geometry --- Differential equations, Partial. --- Équations différentielles elliptiques --- Équations aux dérivées partielles

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"We obtain local boundedness and maximum principles for weak subsolutions to certain infinitely degenerate elliptic divergence form inhomogeneous equations, and also continuity of weak solutions to homogeneous equations. For example, we consider the family {f[sigma]}[sigma]>0 with f[sigma] (x) = e -( 1 [pipe]x[pipe] ) [sigma] , -[infinity]