标题： 拟线性椭圆方程有限能量解的奥尔利奇增长 显示英文标题

标题： Finite energy solutions of quasilinear elliptic equations with Orlicz growth

摘要： 我们给出了一个充分条件（用Wolff位势表达），用于度量数据的$(p,q)$-Laplacian 方程具有“次线性增长”速率的有限能量解的存在性。此外，我们证明了这种解是最小的。另外，即使能量不是有限的，适当地广义的Wolff型位势的一个下界对于解的存在性也是必要的。我们的主要工具包括与度量数据相关的$(p,q)$-Laplacian 方程的积分不等式和点位势估计，这对于建立此类问题解的存在性至关重要。这种方法还使我们能够解决涉及广义拟线性算子的其他非线性椭圆问题。 显示英文摘要

摘要： We present a sufficient condition, expressed in terms of Wolff potentials, for the existence of a finite energy solution to the measure data $(p,q)$-Laplacian equation with a "sublinear growth" rate. Furthermore, we prove that such a solution is minimal. Additionally, a lower bound of a suitably generalized Wolff-type potential is necessary for the existence of a solution, even if the energy is not finite. Our main tools include integral inequalities closely associated with $(p,q)$-Laplacian equations with measure data and pointwise potential estimates, which are crucial for establishing the existence of solutions to this type of problem. This method also enables us to address other nonlinear elliptic problems involving a general class of quasilinear operators.