$L^p$-Variational Solutions of Multivalued Backward Stochastic Differential Equations

The aim of the paper is to prove the existence and uniqueness of the $L^p$–variational solution, with $p>1,$ of the following multivalued backward stochastic differential equation with $p$–integrable data: \begin{equation*} \left{ \begin{array}[c]{l} -dY_{t}+\partial_{y}\Psi(t,Y_{t})dQ_{t}\ni H(t,Y_{t},Z_{t})dQ_{t}-Z_{t}dB_{t},;0\leq t<\tau,\[0.1cm] Y_{\tau}=\eta, \end{array} \right. \end{equation*} where $\tau$ is a stopping time, $Q$ is a progresivelly measurable increasing continuous stochastic process and ${\mathrm{\partial }}_y\mathrm{\Psi }$ is the subdifferential of the convex lower semicontinuous function $y\mapsto \mathrm{\Psi }(t,y)\mathrm{.}$