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The paper concerns a resonance problem for a class of singular quasilinear elliptic equations in weighted Sobolev spaces. The equation set studied is one of the most useful sets of Navier–Stokes equations; these describe the motion of viscous fluid substances such as liquids, gases and so on. By using Galerkin-type techniques, the Brouwer fixed point theorem, and a new weighted compact Sobolev-type...
In this paper, we study the Euler equations and derive approximations of the minimizers for a Heisenberg group target. There are some techniques in the arguments for proving the results. This is in order to overcome the obstacles which are due to the nonlinear structure of the group laws.
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