IAM2012:P000030

$W^{m,p}$-Solution ($p\geq2$) of Linear Degenerate Backward Stochastic Partial Differential Equations in the Whole Space

杜恺 (复旦大学数学科学学院)
汤善健 (复旦大学数学科学学院)
*张奇 (复旦大学数学科学学院)

The backward Cauchy problem of linear degenerate stochastic partial differential equations is discussed in this talk. We obtain the existence and uniqueness results in Sobolev space $L^p(\Omega;C([0,T];W^{m,p}))$ with both $m\geq1$ and $p\geq2$ being arbitrary, without imposing the symmetry condition for the coefficient $\sigma$ of the gradient of the second unknown---which was introduced by Ma and Yong [PTRF 113 (1999)] in the case of $p=2$. To illustrate the application, we give a maximum principle for optimal control of degenerate stochastic partial differential equations. (This is a joint work with Prof. Shanjian Tang and Dr. Kai Du)

The backward Cauchy problem of linear degenerate stochastic partial differential equations is discussed in this talk. We obtain the existence and uniqueness results in Sobolev space $L^p(\Omega;C([0,T];W^{m,p}))$ with both $m\geq1$ and $p\geq2$ being arbitrary, without imposing the symmetry condition for the coefficient $\sigma$ of the gradient of the second unknown---which was introduced by Ma and Yong [PTRF 113 (1999)] in the case of $p=2$. To illustrate the application, we give a maximum principle for optimal control of degenerate stochastic partial differential equations. (This is a joint work with Prof. Shanjian Tang and Dr. Kai Du)

中国工业与应用数学学会第十二届年会

$W^{m,p}$-Solution ($p\geq2$) of Linear Degenerate Backward Stochastic Partial Differential Equations in the Whole Space