共查询到20条相似文献,搜索用时 15 毫秒
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《Comptes Rendus Mathematique》2019,357(9):693-696
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《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2021,38(5):1337-1371
In this paper we consider minimizers of the functional where is a bounded open set and where are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets have finite perimeter and that their free boundary is composed of a regular part, which is locally the graph of a -regular function, and a singular part, which is empty if , discrete if and of Hausdorff dimension at most if , for some . 相似文献
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Let , where Ω is a bounded open subset of . We consider the parabolic p-capacity on Q naturally associated with the usual p-Laplacian. Droniou, Porretta, and Prignet have shown that if a bounded Radon measure μ on Q is diffuse, i.e. charges no set of zero p-capacity, , then it is of the form for some , and . We show the converse of this result: if , then each bounded Radon measure μ on Q admitting such a decomposition is diffuse. 相似文献
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We explicitly determine generators of cyclic codes over a non-Galois finite chain ring of length , where p is a prime number and k is a positive integer. We completely classify that there are three types of principal ideals of and four types of non-principal ideals of , which are associated with cyclic codes over of length . We then obtain a mass formula for cyclic codes over of length . 相似文献
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Masoumah Al-Ali 《Journal of Pure and Applied Algebra》2019,223(12):5430-5443
Let be a simple, finite-dimensional complex Lie algebra, and let denote the universal affine vertex algebra associated to at level k. The Cartan involution on lifts to an involution on , and we denote by the orbifold, or fixed-point subalgebra, under this involution. Our main result is an explicit minimal strong finite generating set for for generic values of k. 相似文献
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Shai Shechter 《Journal of Pure and Applied Algebra》2019,223(10):4384-4425
Let be a complete discrete valuation ring with finite residue field of odd characteristic, and let G be a symplectic or special orthogonal group scheme over . For any let denote the ?-th principal congruence subgroup of . An irreducible character of the group is said to be regular if it is trivial on a subgroup for some ?, and if its restriction to consists of characters of minimal -stabilizer dimension. In the present paper we consider the regular characters of such classical groups over , and construct and enumerate all regular characters of , when the characteristic of is greater than two. As a result, we compute the regular part of their representation zeta function. 相似文献
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