Using some nonlinear domain decomposition method, we prove the existence of singular limits for solution of semilinear elliptic problems with exponential nonlinearity.

In this note, the authors resolve an evolutionary Wente's problem associated to heat equation, where the special integrability of det∇u for u ∈ H 1 (R 2 , R 2 ) is used.

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We study the best constant involving theL2norm of thep-derivative solution of Wente's problem inℝ2p. We prove that this best constant is achieved by the choice of some functionu. We give also explicitly the expression of this constant in the special casep=2.