Visualizing Fluid Flows via Regularized Optimal Mass Transport with Applications to Neuroscience. [PDF]
J Sci Comput, 2023 Chen X +4 more
europepmc +1 more source
New multiplicity results in prescribing Q-curvature on standard spheres
Advanced Nonlinear StudiesIn this paper, we study the problem of prescribing Q-Curvature on higher dimensional standard spheres. The problem consists in finding the right assumptions on a function K so that it is the Q-Curvature of a metric conformal to the standard one on the ...
Ben Ayed Mohamed, El Mehdi Khalil
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Non-critical dimensions for critical problems involving fractional Laplacians [PDF]
arXiv, 2013 We study the Brezis--Nirenberg effect in two families of noncompact boundary value problems involving Dirichlet-Laplacian of arbitrary real order $m>0$.
arxiv
Advanced Nonlinear StudiesWe investigate the following fractional p-Laplacian convex-concave problem:(Pλ)(−Δ)psu=λ|u|q−2u+|u|ps*−2u inΩ,u=0 inRn\Ω, $$\left({P}_{\lambda }\right) \begin{cases}\begin{aligned}\hfill {\left(-{\Delta}\right)}_{p}^{s}u& =\lambda \vert u{\vert
Ye Dong, Zhang Weimin
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Multilinear Embedding and Hardy's Inequality [PDF]
arXiv, 2013 Multilinear trace restriction inequalities are obtained for Hardy's inequality. More generally, detailed development is given for new multilinear forms for Young's convolution inequality, and a new proof for the multilinear Hardy-Littlewood-Sobolev inequality, and its realization on hyperbolic space.
arxiv
Enforcing Dirichlet boundary conditions in physics-informed neural networks and variational physics-informed neural networks. [PDF]
Heliyon, 2023 Berrone S +3 more
europepmc +1 more source
Advanced Nonlinear StudiesIn this paper, we study the following fractional Schrödinger–Poisson system with discontinuous nonlinearity:ε2s(−Δ)su+V(x)u+ϕu=H(u−β)f(u),inR3,ε2s(−Δ)sϕ=u2,inR3,u>0,inR3, $$\begin{cases}^{2s}{\left(-{\Delta}\right)}^{s}u+V\left(x\right)u+\phi u=H\left(u-\
Mu Changyang, Yang Zhipeng, Zhang Wei
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Multiple Solutions for Superlinear Fractional Problems via Theorems of Mixed Type
Advanced Nonlinear Studies, 2018 In this paper, we investigate the existence of multiple solutions for the following two fractional problems:
Ambrosio Vincenzo
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Integrals of convex functions in the gradients on fractals [PDF]
arXiv, 2013 In this paper, I describe the construction of certain functional integrals in the gradient on finitely ramified fractals, which have a sort of self-similarity property.
arxiv
Poly(dA:dT) Tracts Differentially Modulate Nucleosome Remodeling Activity of RSC and ISW1a Complexes, Exerting Tract Orientation-Dependent and -Independent Effects. [PDF]
Int J Mol Sci, 2023 Amigo R +4 more
europepmc +1 more source