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

We propose a theory of non-differentiable solutions which applies to fully nonlinear PDE systems and extends the viscosity Crandall–Ishii–Lions vectorial case. Our key ingredient is discovery notion extremum for maps min-max allows “nonlinear passage derivatives” test maps. This new approach supports certain stability convergence results, preserving some basic features scalar counterpart. In this introductory work, we focus on studying analytical foundations theory.