【摘要】 本文研究一类有偏无穷Laplace方程,它来源于随机博弈论中的有偏二人零和博弈.本文建立该方程解的各种性质,包括解的梯度估计、非负解u及其梯度模|Du|的Harnack不等式.最后,本文证明非常数的C~2光滑解没有内部临界点.更多还原

【Abstract】 In this paper, we study a kind of infinity Laplacian equations arising from biased tug-of-war in random games. Various properties of the solutions for such equations, including the gradient estimates, the Harnack inequalities for both nonnegative u and the gradient |Du|, are established. Finally, we prove that there are no interior critical points for non-constant C~2 solutions.更多还原