Wolff potentials and measure data vectorial problems with Orlicz growth

Wolff potential estimates for supersolutions of equations with generalized Orlicz growth

In this paper, we establish pointwise estimates for supersolutions of quasilinear elliptic equations with structural conditions involving a generalized Orlicz growth in terms of a Wolff type potential. As a consequence, under the extra assumption, we obtain that the supersolutions satisfy a Harnack inequality and local Hölder continuity.

Wolff potentials and local behaviour of solutions to measure data elliptic problems with Orlicz growth

We establish pointwise estimates expressed in terms of a nonlinear potential of a generalized Wolff type for $A$-superharmonic functions with nonlinear operator $A:Ω\times\mathbb{R}^n\to\mathbb{R}^n$ having measurable dependence on the spacial variable and Orlicz growth with respect to the last variable. The result is sharp as the same potential controls bounds from above and from below. Applying it we provide a bunch of precise regularity results including continuity and Hölder continuity for solutions to problems involving measures that satisfies conditions expressed in the natural scales. F…

具有广义Orlicz增长的椭圆障碍问题的Wolff势估计

Wolff potential estimates for elliptic obstacle problems with generalized Orlicz growth

研究具有广义Orlicz增长的椭圆障碍问题，通过建立解在Musielak-Orlicz空间的存在性，利用非线性Wolff势导出解的梯度估计，得到解的$C^{1,\alpha}$正则性结果。

具有Orlicz增长的非局部方程的Wolff位势估计与Wiener准则

Wolff potential estimates and Wiener criterion for nonlocal equations with Orlicz growth

该研究针对具有Orlicz增长的非局部方程，通过非局部非线性位势理论下的上调和函数精细分析，证明了Wolff位势估计，并由此得到刻画边界点正则充要条件的Wiener准则。

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.

具有 Orlicz 增长的拟线性椭圆方程的有限能量解

Finite energy solutions of quasilinear elliptic equations with Orlicz growth

本文利用 Wolff 位势给出带测度数据的次线性增长 $(p,q)$-Laplacian 方程存在有限能量最小解的充分条件，并证明推广 Wolff 型位势下界的必要性，同时将方法推广到一般拟线性椭圆问题。