Results 51 to 60 of about 371 (68)

On Kirchhoff-Schrödinger-Poisson-type systems with singular and critical nonlinearity

Advances in Nonlinear Analysis
This work focuses on the Kirchhoff-Schrödinger-Poisson-type system with singular term and critical Sobolev nonlinearity as follows: −a+b∫Ω∣∇u∣pdxΔpu+ϕ∣u∣q−2u=λu−γ+∣u∣p∗−2uinΩ,−Δϕ=∣u∣qinΩ,u=ϕ=0on∂Ω,\left\{\begin{array}{ll}-\left(a+b\mathop{\displaystyle ...
Yang Baoling, Zhang Deli, Liang Sihua
doaj   +1 more source

Local and nonlocal 1-Laplacian in Carnot groups [PDF]

arXiv, 2020
We formulate and study the nonlocal and local least gradient problem, which is the Dirichlet problem for the 1-Laplace operator, in a quite natural setting of Carnot groups. We study the passage from the nonlocal problem to the local problem as the range of the interaction goes to zero; to do this, we first prove a total variation estimate of ...
arxiv  

Bishop and Laplacian Comparison Theorems on Three Dimensional Contact Subriemannian Manifolds with Symmetry [PDF]

arXiv, 2011
We prove a Bishop volume comparison theorem and a Laplacian comparison theorem for three dimensional contact subriemannian manifolds with symmetry.
arxiv  

Bourgain-Brezis-Mironescu approach in metric spaces with Euclidean tangents [PDF]

arXiv, 2020
In the setting of metric measure spaces satisfying the doubling condition and the $(1,p)$-Poincar\'e inequality, we prove a metric analogue of the Bourgain-Brezis-Mironescu formula for functions in the Sobolev space $W^{1,p}(X,d,\nu)$, under the assumption that for $\nu$-a.e. point the tangent space in the Gromov-Hausdorff sense is Euclidean with fixed
arxiv  

A mean value formula of sub-p-Laplace parabolic equations on the Heisenberg group [PDF]

arXiv, 2013
We derive two equivalent definitions of the viscosity solutions to the homogeneous sub-p- Laplace parabolic equations on the Heisenberg group, and characterize the viscosity solutions in terms of an asymptotic mean value formula. Moreover, we construct an example to show that these formulae do not hold in non-asymptotic sense.
arxiv  

Function Spaces via Fractional Poisson Kernel on Carnot Groups and Applications [PDF]

arXiv, 2020
We provide a new characterization of homogeneous Besov and Sobolev spaces in Carnot groups using the fractional heat kernel and Poisson kernel. We apply our results to study commutators involving fractional powers of the sub-Laplacian.
arxiv  

Schauder estimates for solutions of sub-Laplace equations with Dini terms [PDF]

arXiv, 2014
In this paper we establish Schauder estimates for the sublalpace equation \[\Sigma_{j = 1}^mX_j^2u = f,\] where ${X_1},{X_2}, \ldots ,{X_m}$ is a system of smooth vector field which generates the first layer in the Lie algebra of a Carnot group. We drive the estimate for the second order derivatives of the solution to the equation with Dini continue ...
arxiv  

Variational framework and Lewy-Stampacchia type estimates for nonlocal operators on Heisenberg group [PDF]

arXiv, 2020
The aim of this article is to derive some Lewy-Stampacchia estimates and existence of solutions for equations driven by a nonlocal integro-differential operator on the Heisenberg group.
arxiv  

Existence of optimizers of the Stein-Weiss inequalities on Carnot groups [PDF]

arXiv, 2014
This paper proves existence of optimizers of the Stein-Weiss inequalities on Carnot groups under some conditions. The adjustment of Lions' concentration compactness principles to Carnot groups plays an important role in our proof. Unlike known treatment to the Hardy-Littlewood-Sobolev inequality on Heisenberg group, our arguments relate to the powers ...
arxiv  

Biharmonic functions on the special unitary group SU(2) [PDF]

arXiv, 2016
We construct new proper biharmonic functions defined on open and dense subsets of the special unitary group SU(2). Then we employ a duality principle to obtain new proper biharmonic functions from the non-compact 3-dimensional hyperbolic space H^3.
arxiv