Results 131 to 140 of about 31,104 (274)

Maximum and anti-maximum principles for the p-Laplacian with a nonlinear boundary condition

Electronic Journal of Differential Equations, 2006
In this paper we study the maximum and the anti-maximum principles for the problem $Delta _{p}u=|u|^{p-2}u$ in the bounded smooth domain $Omega subset mathbb{R}^{N}$, with $|abla u|^{p-2}frac{partial u}{partial u }=lambda |u|^{p-2}u+h$ as a non linear ...
Aomar Anane, Omar Chakrone, Najat Moradi
doaj  

p-Laplacians for Manifold-Valued Hypergraphs

Hypergraphs extend traditional graphs by enabling the representation of N-ary relationships through higher-order edges. Akin to a common approach of deriving graph Laplacians, we define function spaces and corresponding symmetric products on the nodes and edges to derive hypergraph Laplacians.
Jo Andersson Stokke, Ronny Bergmann, Martin Hanik, Christoph von Tycowicz   +3 more
openaire   +2 more sources

Higher differentiability for the fractional p-Laplacian

Mathematische Annalen
Abstract In this work, we study the higher differentiability of solutions to the inhomogeneous fractional p-Laplace equation under different regularity assumptions on the data. In the superquadratic case, we extend and sharpen several previous results, while in the subquadratic regime our results constitute completely novel developments even ...
Diening, Lars, Kim, Kyeongbae, Lee, Ho-Sik, Nowak, Simon Noah   +3 more
openaire   +3 more sources

In Vivo Mapping of Catecholaminergic Loss and Iron Deposition in Huntington's Disease

Movement Disorders, EarlyView.
Abstract Background The pathophysiology of Huntington's disease (HD) remains obscure. Magnetic resonance imaging (MRI) can reveal in vivo molecular changes related to disease pathology. Objectives To investigate catecholaminergic neuronal integrity and subcortical brain iron accumulation in HD employing neuromelanin‐sensitive MRI, and quantitative ...
Edoardo R. de Natale, Heather Wilson, Efstratios Karavasilis, Athanasia Liozidou, Chrisoula Kartanou, Georgios Velonakis, Jens Kuhle, Ioannis Zalonis, Georgia Karadima, Leonidas Stefanis, Georgios Koutsis, Marios Politis   +11 more
wiley   +1 more source

Shape Derivatives of the Eigenvalues of the De Rham Complex for Lipschitz Deformations and Variable Coefficients: Part I

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT We study eigenvalue problems for the de Rham complex on varying three‐dimensional domains. Our analysis includes the Helmholtz equation as well as the Maxwell system with mixed boundary conditions and non‐constant coefficients. We provide Hadamard‐type formulas for the shape derivatives under weak regularity assumptions on the domain and its ...
Pier Domenico Lamberti, Dirk Pauly, Michele Zaccaron   +2 more
wiley   +1 more source

Asymptotics for the Spectrum of the Laplacian in Thin Bars with Varying Cross Sections

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT We consider spectral problems for the Laplace operator in 3D rod structures with a small cross section of diameter O(ε)$$ O\left(\varepsilon \right) $$, ε$$ \varepsilon $$ being a positive parameter. The boundary conditions are Dirichlet (Neumann, respectively) on the bases of this structure, and Neumann on the lateral boundary.
Pablo Benavent‐Ocejo, Delfina Gómez, Maria‐Eugenia Pérez‐Martínez   +2 more
wiley   +1 more source

Matsumura‐Type Estimates and Global Solutions of a Fractional Wave Equation With Nonlocal Nonlinearity

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT The main results of this paper are the global existence and long time behavior of solutions of a fractional wave equation with a nonlocal nonlinearity. The techniques in this work rely on norm estimates of the solutions of εutt+ut+(−Δ)βu=0,u(0,x)=φ(x),ut(0,x)=ψ(x),$$ \varepsilon {u}_{tt}+{u}_t+{\left(-\Delta \right)}^{\beta }u=0,\kern1em u ...
Ibrahim Ahmad Suleman, Mokhtar Kirane
wiley   +1 more source

Numerical Investigation of a Diffusive SIR Model: Focus on Positivity Preservation

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT In this paper, we consider a system of semilinear partial differential equations (PDEs) representing a spatially extended SIR epidemic model. A brief analytical investigation of the well‐posedness and positivity of the solutions is provided in the appendix, while the main focus is on the numerical treatment of the model.
Rahele Mosleh, Claudia Panico, Messoud Efendiyev   +2 more
wiley   +1 more source

Positive solutions for singular nonlinear beam equation

Electronic Journal of Differential Equations, 2007
In this paper, we study the existence of solutions for the singular p-Laplacian equation $$displaylines{ ig(|u''|^{p-2}u''ig)''-f(t,u)=0,quad tin (0,1) cr u(0)=u(1)=0, cr u''(0)=u''(1)=0, }$$ where $f(t,u)$ is singular at $t=0,1$ and at $u=0$.
Ruhao Song, Haishen Lu
doaj  

The uniqueness of a nonlinear diffusion equation related to the p-Laplacian. [PDF]

J Inequal Appl, 2018
Zhan H.
europepmc   +1 more source