A SCHAUDER APPROACH TO DEGENERATE-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH UNBOUNDED COEFFICIENTS
A SCHAUDER APPROACH TO DEGENERATE-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH UNBOUNDED COEFFICIENTS
复制标题
具有无界系数的简并抛物型偏微分方程的Schauder方法
DOI：
10.1016/j.jde.2013.03.006
复制
发表时间：
2011
影响因子：
2.4
通讯作者：
C. Pop
中科院分区：
文献类型：
--
作者：
P. Feehan;C. Pop
受概率论和数学金融学的启发，我们考虑了半空间上的一类抛物型偏微分方程解，它的系数是适当的Hölder连续的，并且允许它在空间变量中线性增长，并且沿着半空间的边界退化。我们在加权Hölder空间中建立了解的存在唯一性，其中包含了系数在边界上的退化性和无界性。在我们的伴文(Feehan and Pop[12])中，我们应用本文的主要结果证明了退化椭圆型偏微分算子所对应的鞅问题在Stroock和Varadhan意义下是适定的。
Motivated by applications to probability and mathematical finance, we consider a parabolic partial differential equation on a half-space whose coefficients are suitably Hölder continuous and allowed to grow linearly in the spatial variable and which become degenerate along the boundary of the half-space. We establish existence and uniqueness of solutions in weighted Hölder spaces which incorporate both the degeneracy at the boundary and the unboundedness of the coefficients. In our companion article (Feehan and Pop [12]), we apply the main result of this article to show that the martingale problem associated with a degenerate-elliptic partial differential operator is well-posed in the sense of Stroock and Varadhan.