On a vector-valued generalisation of viscosity solutions for general PDE systems (Q2107771)

This paper develops a new approach of extending the viscosity solution theory for scalar fully nonlinear partial differential equations to the vectorial case. In contrast to the known results on weakly coupled monotone systems, the generlaized notion of vectorial solutions proposed in this work, called contact solutions, can be applied to general non-monotone systems. This paper introduces the basics of such generalization, including the notion of contact jets, the definition and regularity of contact solutions and the relation with classical solutions. A result on the approximation and stability of contact jets is also provided.