Viscosity solutions, almost everywhere solutions and explicit formulas
Bernard Dacorogna, Paolo Marcellini · Transactions of the American Mathematical Society · 2004
Consider the differential inclusion $Du\in E$ in $\mathbb {R}^{n}$. We exhibit an explicit solution that we call fundamental. It also turns out to be a viscosity solution when properly defining this notion. Finally, we consider a Dirichlet problem associated to the differential inclusion and we give an iterative procedure for finding a solution.