Abstract:The influence of the geometry of the domain on the behavior of generalized solutions of Dirichlet problems for elliptic partial differential equations has been an important subject for over a century. We investigate the boundary behavior of variational solutions f of Dirichlet problems for prescribed mean curvature equations in a domain Ω ⊂ R 2 near a point O ∈ ∂Ω under different assumptions about the curvature of ∂Ω on each side of O. We prove that the radial limits at O of f exist under different assumptions… Show more
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