A C1,α$C^{1,\alpha}$ partial regularity result for integral functionals with p⁢(x)$p(x)$-growth condition

AbstractWe establish${C^{1,\alpha}}$partial regularity for the local minimizers of integral functionals of the type$\mathcal{F}(u;\Omega):=\int_{\Omega}(1+|Du|^{2})^{\frac{p(x)}{2}}\,dx,$where the gradient of the exponent function${p(\,\cdot\,)\geq 2}$belongs to a suitable Orlicz–Zygmund class.

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A Partial Regularity Result for the Combined Total Variation Functional for Image Restoration

2010 International Conference on Computational and Information Sciences ◽

10.1109/iccis.2010.289 ◽

2010 ◽

Author(s):

Dong-Hong Zhao ◽

Lai-Sheng Wang

Keyword(s):

Image Restoration ◽

Total Variation ◽

Partial Regularity ◽

Regularity Result ◽

Partial Regularity Result

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RETRACTED ARTICLE: A $${C^{1,\alpha}}$$ partial regularity result for non-autonomous convex integrals with discontinuous coefficients

Nonlinear Differential Equations and Applications NoDEA ◽

10.1007/s00030-015-0324-3 ◽

2015 ◽

Vol 22 (5) ◽

pp. 1319-1343 ◽

Cited By ~ 8

Author(s):

Antonia Passarelli di Napoli

Keyword(s):

Partial Regularity ◽

Regularity Result ◽

Discontinuous Coefficients ◽

Retracted Article ◽

Partial Regularity Result

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A new partial regularity result for non-autonomous convex integrals with non-standard growth conditions

Journal of Differential Equations ◽

10.1016/j.jde.2010.09.033 ◽

2011 ◽

Vol 250 (3) ◽

pp. 1363-1385 ◽

Cited By ~ 7

Author(s):

Bruno De Maria ◽

Antonia Passarelli di Napoli

Keyword(s):

Partial Regularity ◽

Regularity Result ◽

Growth Conditions ◽

Partial Regularity Result

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A partial regularity result for an anisotropic smoothing functional for image restoration in BV space

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2007.07.013 ◽

2008 ◽

Vol 339 (2) ◽

pp. 1169-1178 ◽

Cited By ~ 2

Author(s):

Thomas Wunderli

Keyword(s):

Image Restoration ◽

Partial Regularity ◽

Regularity Result ◽

Partial Regularity Result ◽

Anisotropic Smoothing

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Partial regularity result for non-autonomous elliptic systems with general growth

Communications on Pure and Applied Analysis ◽

10.3934/cpaa.2021160 ◽

2021 ◽

Vol 0 (0) ◽

pp. 0

Author(s):

Teresa Isernia ◽

Chiara Leone ◽

Anna Verde

Keyword(s):

Weak Solutions ◽

Partial Regularity ◽

Elliptic Systems ◽

Regularity Result ◽

Crucial Point ◽

Weak Regularity ◽

General Growth ◽

Regularity Properties ◽

Controllable Growth ◽

Partial Regularity Result

In this paper we prove a partial Hölder regularity result for weak solutions <inline-formula><tex-math id="M1">\begin{document}$ u:\Omega\to \mathbb{R}^N $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ N\geq 2 $\end{document}</tex-math></inline-formula>, to non-autonomous elliptic systems with general growth of the type:<disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} -{\rm{div}} a(x, u, Du) = b(x, u, Du) \quad \;{\rm{ in }}\; \Omega. \end{equation*} $\end{document} </tex-math></disp-formula>The crucial point is that the operator <inline-formula><tex-math id="M3">\begin{document}$ a $\end{document}</tex-math></inline-formula> satisfies very weak regularity properties and a general growth, while the inhomogeneity <inline-formula><tex-math id="M4">\begin{document}$ b $\end{document}</tex-math></inline-formula> has a controllable growth.

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