4 citations · 6 across the 15 of their papers we have counts for
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Asymptotics of solutions to the porous medium equation near conical singularities
Nikolaos Roidos, Elmar Schrohe
We show that, on a manifold with conical singularities, the asymptotics of the solutions to the porous medium equation near the conical points are determined by the spectrum of the…
The spectrum of the Laplacian on closed manifolds and the heat asymptotics near conical points
Nikolaos Roidos
Let be a smooth, closed and connected manifold of dimension , endowed with a Riemannian metric . Moreover, let be an -dimensio…
Maximal -regularity for the Laplacian on manifolds with edges
Nikolaos Roidos
We introduce an -sectoriality perturbation technique for non-commuting operators defined in Bochner spaces. Based on this and on bounded -functional calculus results…
Existence of global attractors and convergence of solutions for the Cahn-Hilliard equation on manifolds with conical singularities
Pedro T. P. Lopes, Nikolaos Roidos
We consider the Cahn-Hilliard equation on manifolds with conical singularities and prove existence of global attractors in higher order Mellin-Sobolev spaces with asymptotics. We a…
Maximal -regularity of nonlocal parabolic equations in higher order Bessel potential spaces
Nikolaos Roidos, Yuanzhen Shao
We consider fractional parabolic equations with variable coefficients and establish maximal -regularity in Bessel potential spaces of arbitrary nonnegative order. As an appl…
Functional Inequalities involving Nonlocal Operators on Complete Riemannian Manifolds and Their Applications to The Fractional Porous Medium Equation
Nikolaos Roidos, Yuanzhen Shao
The objective of this paper is twofold. First, we conduct a careful study of various functional inequalities involving the fractional Laplacian operators, including nonlocal Sobole…
The fractional porous medium equation on manifolds with conical singularities II
Nikolaos Roidos, Yuanzhen Shao
This is the second of a series of two papers which studies the fractional porous medium equation, with and , posed on a Rie…
The fractional porous medium equation on manifolds with conical singularities I
Nikolaos Roidos, Yuanzhen Shao
This is the first of a series of two papers which studies the fractional porous medium equation on a Riemannian manifold with isolated conical singularities. In this article, we sh…
Bounded -calculus for Boundary Value Problems on Manifolds with Conical Singularities
Nikolaos Roidos, Elmar Schrohe, Jörg Seiler
Realizations of differential operators subject to differential boundary conditions on manifolds with conical singularities are shown to have a bounded -calculus in appr…
Smoothness and long time existence for solutions of the Cahn-Hilliard equation on manifolds with conical singularities
Pedro T. P. Lopes, Nikolaos Roidos
We consider the Cahn-Hilliard equation on manifolds with conical singularities. For appropriate initial data, we show that the solution exists in the maximal -regularity space…
Conic manifolds under the Yamabe flow
Nikolaos Roidos
We consider the unnormalized Yamabe flow on manifolds with conical singularities. Under certain geometric assumption on the initial cross-section we show well posedness of the shor…
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…
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…
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…
The Swift-Hohenberg equation on conic manifolds
Nikolaos Roidos
We consider the Swift-Hohenberg equation on manifolds with conical singularities and show existence, uniqueness and maximal regularity of the short time solution in terms of Mellin…
Existence and maximal -regularity of solutions for the porous medium equation on manifolds with conical singularities
Nikolaos Roidos, Elmar Schrohe
We consider the porous medium equation on manifolds with conical singularities and show existence, uniqueness and maximal -regularity of a short time solution. In particular…
Bounded imaginary powers of cone differential operators on higher order Mellin-Sobolev spaces and applications to the Cahn-Hilliard equation
Nikolaos Roidos, Elmar Schrohe
Extending earlier results on the existence of bounded imaginary powers for cone differential operators on weighted -spaces over a manifold wi…
The Cahn-Hilliard Equation and the Allen-Cahn Equation on Manifolds with Conical Singularities
Nikolaos Roidos, Elmar Schrohe
We consider the Cahn-Hilliard equation on a manifold with conical singularities and show the existence of bounded imaginary powers for suitable closed extensions of the bilaplacian…