N. Roidos

activity

20122026

L^{p}

-regularity of solutions for the porous medium equation on manifolds with conical singularities

4 citations · 6 across the 15 of their papers we have counts for

collaborators

25 papers

math.FA2026

Strip-type operators and abstract Cauchy problems

Nikolaos Roidos

We consider the non-homogeneous abstract linear Schrödinger and wave equations with zero initial conditions, defined by operators of strip-type and parabola-type in Banach spaces,…

math.AP2025

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…

math.AP2023

The spectrum of the Laplacian on closed manifolds and the heat asymptotics near conical points

Nikolaos Roidos

Let $M$ be a smooth, closed and connected manifold of dimension $n \in N$ , endowed with a Riemannian metric $g$ . Moreover, let $B$ be an $(n + 1)$ -dimensio…

math.AP2023

Maximal $L^{q}$ -regularity for the Laplacian on manifolds with edges

Nikolaos Roidos

We introduce an $R$ -sectoriality perturbation technique for non-commuting operators defined in Bochner spaces. Based on this and on bounded $H^{\infty}$ -functional calculus results…

math.AP2022★ 1 cited

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…

math.AP2021

Maximal $L_{q}$ -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 $L_{q}$ -regularity in Bessel potential spaces of arbitrary nonnegative order. As an appl…

math.AP2020

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…

math.DG2020

Curve shortening flow on Riemann surfaces with conical singularities

Nikolaos Roidos, Andreas Savas-Halilaj

We study the curve shortening flow on Riemann surfaces with finitely many conformal conical singularities. If the initial curve is passing through the singular points, then the evo…

math.AP2019

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, $\partial_{t} u + (- Δ)^{σ} (∣ u ∣^{m - 1} u) = 0$ with $m > 0$ and $σ \in (0, 1]$ , posed on a Rie…

math.AP2019

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…

math.AP2019

Bounded $H_{\infty}$ -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 $H_{\infty}$ -calculus in appr…

math.AP2019

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 $L^{q}$ -regularity space…

math.FA2018

Heinz-Kato inequality in Banach spaces

Nikolaos Roidos

It is observed that in Banach spaces, sectorial operators having bounded imaginary powers satisfy a Heinz-Kato inequality.

math.AP2018

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…

math.AP2017

Expanding solutions of quasilinear parabolic equations

Nikolaos Roidos

By using the theory of maximal $L^{q}$ -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 $L^{q}$ -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 $B$ -elliptic cone differential operators. We apply this result to the hea…

math.AP2016

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…

math.SP2016

A scattering approach to a surface with hyperbolic cusp

Nikolaos Roidos

Let $X$ be a two-dimensional smooth manifold with boundary $S^{1}$ and $Y = [1, \infty) \times S^{1}$ . We consider a family of complete surfaces arising by endowing $X \cup_{S^{1}} Y$ wi…

math.FA2016

Closedness and invertibility for the sum of two closed operators

Nikolaos Roidos

We show a Kalton-Weis type theorem for the general case of non-commuting operators. More precisely, we consider sums of two possibly non-commuting linear operators defined in a Ban…

math.AP2015★ 4 cited

Existence and maximal $L^{p}$ -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 $L^{p}$ -regularity of a short time solution. In particular…

math.AP2013

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 $L^{p}$ -spaces $H_{p}^{0, γ} (B)$ over a manifold wi…

math.FA2013

Preserving closedness of operators under summation

Nikolaos Roidos

We give a sufficient condition for the sum of two closed operators to be closed. In particular, we study the sum of two sectorial operators with the sum of their sectoriality angle…

math.FA2012

On the inverse of the sum of two sectorial operators

Nikolaos Roidos

We study an abstract linear operator equation on a Banach space by using the inverse of the sum of two sectorial operators. We prove that the boundedness of a special type of opera…

Strip-type operators and abstract Cauchy problems

Asymptotics of solutions to the porous medium equation near conical singularities

The spectrum of the Laplacian on closed manifolds and the heat asymptotics near conical points

Maximal Lq-regularity for the Laplacian on manifolds with edges

Existence of global attractors and convergence of solutions for the Cahn-Hilliard equation on manifolds with conical singularities

Maximal Lq​-regularity of nonlocal parabolic equations in higher order Bessel potential spaces

Functional Inequalities involving Nonlocal Operators on Complete Riemannian Manifolds and Their Applications to The Fractional Porous Medium Equation

Curve shortening flow on Riemann surfaces with conical singularities

The fractional porous medium equation on manifolds with conical singularities II

The fractional porous medium equation on manifolds with conical singularities I

Bounded H∞​-calculus for Boundary Value Problems on Manifolds with Conical Singularities

Smoothness and long time existence for solutions of the Cahn-Hilliard equation on manifolds with conical singularities

Heinz-Kato inequality in Banach spaces

Conic manifolds under the Yamabe flow

Expanding solutions of quasilinear parabolic equations

Smoothness and long time existence for solutions of the porous medium equation on manifolds with conical singularities

Complex powers for cone differential operators and the heat equation on manifolds with conical singularities

The Swift-Hohenberg equation on conic manifolds

A scattering approach to a surface with hyperbolic cusp

Closedness and invertibility for the sum of two closed operators

Existence and maximal Lp-regularity of solutions for the porous medium equation on manifolds with conical singularities

Bounded imaginary powers of cone differential operators on higher order Mellin-Sobolev spaces and applications to the Cahn-Hilliard equation

Preserving closedness of operators under summation

On the inverse of the sum of two sectorial operators

Maximal $L^{q}$ -regularity for the Laplacian on manifolds with edges

Maximal $L_{q}$ -regularity of nonlocal parabolic equations in higher order Bessel potential spaces

Bounded $H_{\infty}$ -calculus for Boundary Value Problems on Manifolds with Conical Singularities

Existence and maximal $L^{p}$ -regularity of solutions for the porous medium equation on manifolds with conical singularities