Abstract
Let T 2 be a flat two-dimensional torus with fundamental cell domain \(\left[ { - \tfrac{1} {2},\tfrac{1} {2}} \right] \times \left[ { - \tfrac{1} {2},\tfrac{1} {2}} \right]\), h(x) a positive smooth function satisfying the symmetric property (8) on T 2. In this paper we give some sufficient condition under which the mean field equation Δu = 16π − 16πhe u, has a smooth solution.
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Wang, M. A mean field equation with symmetry on torus. Sci. China Math. 54, 2205–2211 (2011). https://doi.org/10.1007/s11425-011-4271-0
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DOI: https://doi.org/10.1007/s11425-011-4271-0