Partial regularity for an exponential PDE in crystal surface models
نویسندگان
چکیده
Abstract We study regularity properties of weak solutions to the boundary value problem for equation −Δ ρ + au = f in a bounded domain Ω ⊂ mathvariant="double-struck">R N , where $\rho ={\mathrm{e}}^{-\text{div}\left(\vert \nabla u{\vert }^{p-2}\nabla u+{\beta }_{0}\vert }^{-1}\nabla u\right)}$?> ρ = mathvariant="normal">e − div | ∇ u p 2 + β 0 1 . This is derived from mathematical modelling crystal surfaces. It known that exponential term can be measure-valued function. In this paper we obtain partial result, which asserts there exists an open subset Ω 0 ⊂ such |Ω\Ω | and locally Furthermore, if x ∈ Ω\Ω then vanishes N 2 − ɛ order at each (0, 2).
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2022
ISSN: ['0951-7715', '1361-6544']
DOI: https://doi.org/10.1088/1361-6544/ac7b62