Results 51 to 60 of about 27,734 (203)

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

On fractional p-Laplacian type equations with general nonlinearities

TURKISH JOURNAL OF MATHEMATICS, 2021
Summary: In this paper, we study the existence and multiplicity of solutions for a class of quasi-linear elliptic problems driven by a nonlocal integro-differential operator with homogeneous Dirichlet boundary conditions. As a particular case, we study the following problem: \[ \begin{cases} (-\Delta)_p^s u= f(x, u) \quad\text{in }\Omega,\\ u=0 \quad ...
Adel DAOUAS, Mohamed LOUCHAICH
openaire   +1 more source

A Unifying Approach to Self‐Organizing Systems Interacting via Conservation Laws

Advanced Intelligent Discovery, EarlyView.
The article develops a unified way to model and analyze self‐organizing systems whose interactions are constrained by conservation laws. It represents physical/biological/engineered networks as graphs and builds projection operators (from incidence/cycle structure) that enforce those constraints and decompose network variables into constrained versus ...
F. Barrows, G. Zhang, S. Anand, Z. Chen, J. Lin, A. Desai, S. Martiniani, F. Caravelli   +7 more
wiley   +1 more source

The fractional Laplacian in power-weighted $L^p$ spaces: integration-by-parts formulas and self-adjointness

, 2016
We consider the fractional Laplacian operator $(-\Delta)^s$ (let $ s \in (0,1) $) on Euclidean space and investigate the validity of the classical integration-by-parts formula that connects the $ L^2(\mathbb{R}^d) $ scalar product between a function and ...
Muratori, Matteo
core   +1 more source

On a coupled system of fractional sum-difference equations with p-Laplacian operator

Advances in Difference Equations, 2020
In this paper, we propose a nonlocal fractional sum-difference boundary value problem for a coupled system of fractional sum-difference equations with p-Laplacian operator. The problem contains both Riemann–Liouville and Caputo fractional difference with
Pimchana Siricharuanun, Saowaluck Chasreechai, Thanin Sitthiwirattham   +2 more
doaj   +1 more source

Composition‐Aware Cross‐Sectional Integration for Spatial Transcriptomics

Advanced Intelligent Discovery, EarlyView.
Multi‐section spatial transcriptomics demands coherent cell‐type deconvolution, domain detection, and batch correction, yet existing pipelines treat these tasks separately. FUSION unifies them within a composition‐aware latent framework, modeling reads as cell‐type–specific topics and clustering in embedding space.
Qishi Dong, Zijian Huang, Xuanwu Wang, Zhenghui Feng, Wei Liu, Bingding Huang   +5 more
wiley   +1 more source

Calderón–Zygmund Estimates for the Fractional p-Laplacian

Annals of PDE
Abstract We prove fine higher regularity results of Calderón-Zygmund-type for equations involving nonlocal operators modelled on the fractional p-Laplacian with possibly discontinuous coefficients of VMO-type. We accomplish this by establishing precise pointwise bounds in terms of certain fractional sharp maximal functions.
Diening, Lars, Nowak, Simon Noah
openaire   +3 more sources

Positive solutions for eigenvalue problems of fractional q-difference equation with ϕ-Laplacian

Advances in Difference Equations, 2021
The aim of this paper is to investigate the boundary value problem of a fractional q-difference equation with ϕ-Laplacian, where ϕ-Laplacian is a generalized p-Laplacian operator. We obtain the existence and nonexistence of positive solutions in terms of
Jufang Wang, Changlong Yu, Boya Zhang, Si Wang   +3 more
doaj   +1 more source

Eigenvalues homogenization for the fractional $p-$Laplacian operator [PDF]

, 2015
In this work we study the homogenization for eigenvalues of the fractional $p-$Laplace in a bounded domain both with Dirichlet and Neumann conditions. We obtain the convergence of eigenvalues and the explicit order of the convergence rates.Comment: 12 ...
Salort, Ariel M.
core  

Nonlocal problems with critical Hardy nonlinearity

, 2018
By means of variational methods we establish existence and multiplicity of solutions for a class of nonlinear nonlocal problems involving the fractional p-Laplacian and a combined Sobolev and Hardy nonlinearity at subcritical and critical growth.Comment:
Chen, Wenjing, Mosconi, Sunra, Squassina, Marco   +2 more
core   +1 more source