p(x)-Harmonic functions with unbounded exponent in a subdomain

Juan J. Manfredi, Julio D. Rossi, José Miguel Urbano

We study the Dirichlet problem $-÷(|\nabla u{|}^{p(x)-2}\nabla u)=0$ in $\Omega$, with $u=f$ on $\partial \Omega$ and $p(x)=\infty$ in $D$, a subdomain of the reference domain $\Omega$. The ma…