Results 61 to 70 of about 1,966 (104)

Besov regularity for solutions of p-harmonic equations

Advances in Nonlinear Analysis, 2017
We establish the higher fractional differentiability of the solutions to nonlinear elliptic equations in divergence form, i.e., div⁡𝒜⁢(x,D⁢u)=div⁡F,{\operatorname{div}\mathcal{A}(x,Du)=\operatorname{div}F,} when 𝒜{\mathcal{A}} is a p-harmonic type ...
Clop Albert, Giova Raffaella, Passarelli di Napoli Antonia   +2 more
doaj   +1 more source

On the continuity of solutions to advection-diffusion equations with slightly super-critical divergence-free drifts

Advances in Nonlinear Analysis, 2014
We address the regularity of solutions to elliptic and parabolic equations of the form -Δu+b·∇u=0${- \Delta u+b\cdot \nabla u=0}$ and ut-Δu+b·∇u=0${u_t- \Delta u+b\cdot \nabla u=0}$ with divergence-free drifts b.
Ignatova Mihaela
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Global strong solution of compressible flow with spherically symmetric data and density-dependent viscosities

Advances in Nonlinear Analysis
In this article, the Cauchy problem of a compressible Navier-Stokes system with density-dependent viscosities when the initial data are spherically symmetric is considered. Firstly, we construct the classical solution for the system in Ba(t)={r:0≤r≤a(t)}{
Guo Zhenhua, Xu Lei, Zhang Xueyao
doaj   +1 more source

Boundary regularity of an isotropically censored nonlocal operator. [PDF]

Calc Var Partial Differ Equ, 2023
Chan H.
europepmc   +1 more source

Regularity of weak solutions to the 3D stationary tropical climate model

Open Mathematics
This article studies the regularity of weak solutions to the 3D stationary tropical climate model. We prove that when (U,V,θ)\left(U,V,\theta ) belongs to the homogeneous Morrey space M˙2,p(R3){\dot{M}}^{2,p}\left({{\mathbb{R}}}^{3}) with p>3p\gt 3, then
Song Huiyang, Bie Qunyi, Zhou Yanping
doaj   +1 more source

The initial-value problem for a Gardner-type equation

Advanced Nonlinear Studies
Discussed here is a regularized version(0.1)ut+ux+uux+Au2ux−uxxt=0, $${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}-{u}_{\mathit{xxt}}=0,$$ of the classical Gardner equationut+ux+uux+Au2ux+uxxx=0, $${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}+{u}_{\mathit{xxx ...
Bona Jerry, Chen Hongqiu, Guerrero Pamela, Haidau Cristina, Pantic Sanja   +4 more
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Nonoccurrence of Lavrentiev gap for a class of functionals with nonstandard growth

Advances in Nonlinear Analysis
We consider the functional ℱ(u)≔∫Ωf(x,Du(x))dx,{\mathcal{ {\mathcal F} }}\left(u):= \mathop{\int }\limits_{\Omega }f\left(x,Du\left(x)){\rm{d}}x, where f(x,z)f\left(x,z) satisfies a (p,q)\left(p,q)-growth condition with respect to zz and can be ...
De Filippis Filomena, Leonetti Francesco, Treu Giulia   +2 more
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Addendum: Local Elliptic Regularity for the Dirichlet Fractional Laplacian

Advanced Nonlinear Studies, 2017
In [1], for ...
Biccari Umberto, Warma Mahamadi, Zuazua Enrique   +2 more
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Nontrivial solutions for resonance quasilinear elliptic systems

Advances in Nonlinear Analysis
We establish an Amann-Zehnder-type result for resonance systems of quasilinear elliptic equations with homogeneous Dirichlet boundary conditions, involving nonlinearities growing asymptotically (p,q)\left(p,q)-linear at infinity.
Borgia Natalino, Cingolani Silvia, Vannella Giuseppina   +2 more
doaj   +1 more source

Sobolev-Kantorovich Inequalities

Analysis and Geometry in Metric Spaces, 2015
In a recent work, E. Cinti and F. Otto established some new interpolation inequalities in the study of pattern formation, bounding the Lr(μ)-norm of a probability density with respect to the reference measure μ by its Sobolev norm and the Kantorovich ...
Ledoux Michel
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