Gradient constraints, Born-Infeld, and maximal surfaces via superposition of infinitely many $p$-Laplacians

We study the Dirichlet problem for an infinite series of $p$-Laplacians, $$-\sum_{p=2}^{\infty}a_{p}Δ_{p}u=f \ \text{ in } Ω, \qquad u=g \ \text{ on } \partialΩ,$$ where $\{a_{p}\}$ is a sequence of nonnegative numbers whose power series has radius of convergence $σ\in(0,\infty]$. The operator is fo