论文标题
第四阶的热内核估计非均匀椭圆算子具有非强凸形符号
Heat kernel estimates for fourth order non-uniformly elliptic operators with non strongly convex symbols
论文作者
论文摘要
我们获得了在二维中非均匀椭圆算子的第四阶级别的热内核估计值。与现有结果相反，所考虑的操作员的符号不是强烈凸出。这引起了某些困难，众所周知，与强凸状的情况相反，没有绝对的指数常数。我们的估计涉及由操作员符号引起的尖锐常数和鳍型距离。主要结果是基于两个一般假设，即加权的Sobolev不平等和插值不平等，这与系数的奇异性或退化有关。
We obtain heat kernel estimates for a class of fourth order non-uniformly elliptic operators in two dimensions. Contrary to existing results, the operators considered have symbols that are not strongly convex. This rises certain difficulties as it is known that, as opposed to the strongly convex case, there is no absolute exponential constant. Our estimates involve sharp constants and Finsler-type distances that are induced by the operator symbol. The main result is based on two general hypotheses, a weighted Sobolev inequalitry and an interpolation inequality, which are related to the singularity or degeneracy of the coefficients.
