Palais-Smale sequence relative to the Trudinger-Moser inequality (Q1404473)

The paper studies a variational approach for elliptic equations with exponential nonlinearities which can be written as the Euler-Lagrange equations of smooth functionals on \(H^1(\Omega)\), where \(\Omega\) is a bounded domain in \(\mathbb{R}^2\). Precisely, it is investigated the behavior of Palais-Smale sequences for the involved functionals showing that they concentrate to finite points if they are not compact in \(H^1(\Omega)\). The optimality of the imposed assumptions is also discussed.