论文标题
双相方程的分布和粘度解决方案之间的等效性
Equivalence between distributional and viscosity solutions for the double-phase equation
论文作者
论文摘要
我们研究了双相方程$$ - \ dive（| du |^{p-2} du+a（x）| du |^{q-2} du）= 0，$$的不同概念的特征是，元素均表征了椭圆度和增长在两种不同类型的多态度之间的事实。我们介绍了$ \ Mathcal {a} _ {h（\ cdot）} $ - 非线性潜在理论的谐波函数，然后表明$ \ Mathcal {a} _ {h（\ cdot）} $ - 谐波函数分别与分布和粘度解决方案相关。这意味着分布和粘度解决方案完全相同。
We investigate the different notions of solutions to the double-phase equation $$ -\dive(|Du|^{p-2}Du+a(x)|Du|^{q-2}Du)=0, $$ which is characterized by the fact that both ellipticity and growth switch between two different types of polynomial according to the position. We introduce the $\mathcal{A}_{H(\cdot)}$-harmonic functions of nonlinear potential theory, and then show that $\mathcal{A}_{H(\cdot)}$-harmonic functions coincide with the distributional and viscosity solutions, respectively. This implies that the distributional and viscosity solutions are exactly the same.
