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math.AP2017
Expanding solutions of quasilinear parabolic equations
Nikolaos Roidos
By using the theory of maximal -regularity and methods of singular analysis, we show a Taylor's type expansion--with respect to the geodesic distance around an arbitrary poi…
math.AP2017
Smoothness and long time existence for solutions of the porous medium equation on manifolds with conical singularities
Nikolaos Roidos, Elmar Schrohe
We study the porous medium equation on manifolds with conical singularities. Given strictly positive initial values, we show that the solution exists in the maximal -regular…
math.AP2017
Complex powers for cone differential operators and the heat equation on manifolds with conical singularities
Nikolaos Roidos
We obtain left and right continuous embeddings for the domains of the complex powers of sectorial -elliptic cone differential operators. We apply this result to the hea…