Multidimensional BSDE with super-linear growth coefficient: application to degenerate systems of semilinear PDEs
The authors consider multidimensional BSDE's and establishes the existence and uniqueness as well as the stability of \(p\)-integrable solutions with super-linear growth coefficient and a \(p\)-integrable terminal condition \((p > 1)\). The main difference is that they do not need the generator to be locally monotone in the \(y\) variable neither locally Lipschitz in the variable \(z\). Finally, they give an application to existence of weak Sobolev solutions to the associated system of semilinear parabolic PDEs.
scientific article; zbMATH DE number 5757883