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In this paper, we consider the backward Cauchy problem of linear degeneratestochastic partial differential equations. We obtain the existence anduniqueness results in Sobolev space $L^p(\Omega; C([0,T];W^{m,p}))$ with both$m\geq 1$ and $p\geq 2$ being arbitrary, without imposing the symmetrycondition for the coefficient $\sigma$ of the gradient of the secondunknown---which was introduced by Ma and Yong [Prob. Theor. Relat. Fields 113(1999)] in the case of $p=2$. To illustrate the application, we give a maximumprinciple for optimal control of degenerate stochastic partial differentialequations.

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