Develops R-sectoriality perturbation for non-commuting operators to establish maximal L^q-regularity of the Laplacian on manifolds with edges and applies it to short-time well-posedness of the porous medium equation.
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Proves well-posedness of classical solutions to abstract linear Schrödinger and wave equations defined by strip-type and parabola-type operators in Banach spaces, with R-boundedness variants and application to semilinear wave equation.
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Maximal $L^{q}$-regularity for the Laplacian on manifolds with edges
Develops R-sectoriality perturbation for non-commuting operators to establish maximal L^q-regularity of the Laplacian on manifolds with edges and applies it to short-time well-posedness of the porous medium equation.
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Strip-type operators and abstract Cauchy problems
Proves well-posedness of classical solutions to abstract linear Schrödinger and wave equations defined by strip-type and parabola-type operators in Banach spaces, with R-boundedness variants and application to semilinear wave equation.