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Lingwei Ma

Publications and source records attributed to Lingwei Ma.

22 records · Page 2Linked to original sources
arXiv2021

Nonlinear Potential Estimates for Generalized Stokes System

In this paper, we consider the generalized stationary Stokes system with $p$-growth and Dini-$\operatorname{BMO}$ regular coefficients. The main purpose is to establish pointwise estimates for the shear rate and the associated pressure to such Stokes system in terms of an unconventional nonlinear Havin-Maz'ya-Wolff type potential of the nonhomogeneous term in the plane. As a consequence, a symmetric gradient $L^{\infty}$ estimate is obtained. Moreover, we derive potential estimates for the weak solution to the Stokes system without additional regularity assumptions on the coefficients in higher dimensional space.

math.AP↗
arXiv2021

Gradient potential estimates in elliptic obstacle problems with Orlicz growth

In this paper,we consider the solutions of the non-homogeneous elliptic obstacle problems with Orlicz growth involving measure data. We first establish the pointwise estimates of the approximable solutions to these problems via fractional maximal operators. As a result, we obtain pointwise and oscillation estimates for the gradients of solutions by the non-linear Wolff potentials, and these yield results on $C^{1,α}$-regularity of solutions.

math.AP↗
arXiv2019

Symmetry and Monotonicity of Positive Solutions to Schrödinger Systems with Fractional $p$-Laplacian

In this paper, we first establish a narrow region principle and a decay at infinity theorem to extend the direct method of moving planes for general fractional $p$-Laplacian systems. By virtue of this method, we can investigate the qualitative properties of the following Schrödinger system with fractional $p$-Laplacian \begin{equation*} \left\{\begin{array}{r@{\ \ }c@{\ \ }ll} \left(-Δ\right)_{p}^{s}u+au^{p-1}& =&f(u,v), \\[0.05cm] \left(-Δ\right)_{p}^{t}v+bv^{p-1}& =&g(u,v), \end{array}\right. \end{equation*} where $0<s,\,t<1$ and $2<p<\infty$. We obtain the radial symmetry in the unit ball or the whole space $\mathbb{R}^{N}(N\geq2)$, the monotonicity in the parabolic domain and the nonexistence on the half space for positive solutions to the above system under some suitable conditions on $f$ and $g$, respectively.

math.AP↗