On interior regularity of minimizers of -energy functionals

Ragusa, Maria Alessandra; Tachikawa, Atsushi

doi:10.1016/j.na.2013.07.023

Cited by 44 publications

(22 citation statements)

References 19 publications

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“…A continuation of the study started by Ragusa, Tachikawa and Takabayashi of partial regularity of minimizers for the above functional under the non-standard growth conditions of p(x)-type, is recently obtained by Ragusa and Tachikawa in the note [24].…”

Section: Theorem 23mentioning

confidence: 89%

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On some regularity results of minimizers of energy functionals

Ragusa

Tachikawa

2014

AIP Conference Proceedings

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Section: Theorem 23mentioning

confidence: 89%

“…To obtain in [24] the announced C 1,α −regularity in the interior for a minimizer of the p(x)−energy functional the authors need the following assumptions, but first we recall that, bearing in mind [30], we know that a minimizer u of the p(x)-energy F is bounded, then exists M > 0 such that u ∞ < M.…”

Section: Theorem 23mentioning

confidence: 99%

On some regularity results of minimizers of energy functionals

Ragusa

Tachikawa

2014

AIP Conference Proceedings

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“…For recent work related to various kinds of difference sequence spaces, we refer to [7][8][9][10][11][12][13] and references therein.…”

Section: Journal Of Function Spacesmentioning

confidence: 99%

Some Seminormed Difference Sequence Spaces over n-Normed Spaces Defined by a Musielak-Orlicz Function of Order (α,β)

Mohiuddine

Sharma

Abuzaid

2018

Journal of Function Spaces

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“…If and V are two weak solutions of (6) with the same partial homogeneous boundary value (13) and ( ( − V)) is chosen to be the test function, then…”

Section: The Stability Of Solutions When < − −1mentioning

confidence: 99%

The Evolutionary p(x)-Laplacian Equation with a Partial Boundary Value Condition

Zhan

Zhen

2018

Discrete Dynamics in Nature and Society

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Consider a diffusion convection equation coming from the electrorheological fluids. If the diffusion coefficient of the equation is degenerate on the boundary, generally, we can only impose a partial boundary value condition to ensure the well-posedness of the solutions. Since the equation is nonlinear, the partial boundary value condition cannot be depicted by Fichera function. In this paper, when α<p--1, an explicit formula of the partial boundary on which we should impose the boundary value is firstly depicted. The stability of the solutions, dependent on this partial boundary value condition, is obtained. While α>p+-1, the stability of the solutions is obtained without the boundary value condition. At the same time, only if α>0 and p->1 can the uniqueness of the solutions be proved without any boundary value condition.

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On interior regularity of minimizers of -energy functionals

Cited by 44 publications

References 19 publications

On some regularity results of minimizers of energy functionals

On some regularity results of minimizers of energy functionals

Some Seminormed Difference Sequence Spaces over n-Normed Spaces Defined by a Musielak-Orlicz Function of Order (α,β)

The Evolutionary p(x)-Laplacian Equation with a Partial Boundary Value Condition

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