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$${\mathscr {A}}$$-quasiconvexity and partial regularity
Calculus of Variations and Partial Differential Equations, 2022 AbstractWe establish the first partial regularity result for local minima of strongly $${\mathscr {A}}$$ A -quasiconvex integrals in the case where the differential operator $${\mathscr {A}}$$ A possesses an elliptic potential $${\mathbb {A}}$$ A . As
Conti, Sergio, Gmeineder, Franz
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Optimal partial regularity of very weak solutions to nonhomogeneous A-harmonic systems [PDF]
Journal of Inequalities and Applications, 2017 We study partial regularity of very weak solutions to some nonhomogeneous A-harmonic systems. To obtain the reverse Hölder inequality of the gradient of a very weak solution, we construct a suitable test function by Hodge decomposition.
Qing Zhao, Shuhong Chen
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Partial Regularity for a Surface Growth Model [PDF]
SIAM Journal on Mathematical Analysis, 2019 We prove two partial regularity results for the scalar equation $u_t+u_{xxxx}+\partial_{xx}u_x^2=0$, a model of surface growth arising from the physical process of molecular epitaxy. We show that the set of space-time singularities has (upper) box-counting dimension no larger than $7/6$ and $1$-dimensional (parabolic) Hausdorff measure zero.
James Robinson +1 more
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Partial regularity for flows of H-surfaces
Electronic Journal of Differential Equations, 1997 This article studies regularity of weak solutions to the heat equation for H-surfaces. Under the assumption that the function H is Lipschitz and depends only on the first two components, the solution has regularity on its domain, except for a set of ...
Changyou Wang
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Partial orders in regular semigroups [PDF]
Proyecciones (Antofagasta), 2011 First we have obtained equivalent conditions for a regular semigroup and is equivalent to N = N1 It is observed that every regular semigroup is weakly separative and C ⊆ S and on a completely regular semigroup S ⊆ N and S is partial order . It is also obtained that a band (S, .) is normal iff C = N .
Srinivas, K. V. R, Anasuya, Y. L
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Regularity and abundance on semigroups of partial transformations with invariant set
Open Mathematics, 2023 Let P(X)P\left(X) be a partial transformation semigroup on a non-empty set XX. For a fixed non-empty subset YY of XX, let PT¯(X,Y)={α∈P(X)∣(domα∩Y)α⊆Y}.\overline{PT}\left(X,Y)=\left\{\alpha \in P\left(X)| \left({\rm{dom}}\hspace{0.33em}\alpha \cap Y ...
Pantarak Thapakorn, Chaiya Yanisa
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Optimal partial regularity for very weak solutions to a class of nonlinear elliptic systems
Journal of Inequalities and Applications, 2023 We consider optimal partial regularity for very weak solutions to a class of nonlinear elliptic systems and obtain the general criterion for a very weak solution to be regular in the neighborhood of a given point.
Shuhong Chen, Zhong Tan
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Minus partial order in regular modules [PDF]
Communications in Algebra, 2020 15 ...
Ungor, B. +3 more
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Partial Enumeration and Curvature Regularization [PDF]
2013 IEEE International Conference on Computer Vision, 2013 Energies with high-order non-sub modular interactions have been shown to be very useful in vision due to their high modeling power. Optimization of such energies, however, is generally NP-hard. A naive approach that works for small problem instances is exhaustive search, that is, enumeration of all possible labelings of the underlying graph. We propose
Olsson, Carl +3 more
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Partial regularity of stable solutions to the fractional Geľfand-Liouville equation
Advances in Nonlinear Analysis, 2021 We analyze stable weak solutions to the fractional Geľfand ...
Hyder Ali, Yang Wen
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