论文标题
$ p（\ cdot）$ - 增长的自由透视问题的整体表示和$γ$ - 融合
Integral representation and $Γ$-convergence for free-discontinuity problems with $p(\cdot)$-growth
论文作者
论文摘要
在可变指数$ p（x）$的log-hölder连续性的假设下，证明了在空间$ gsbv^{p（\ cdot）} $上定义的一般特殊函数的自由透视能量的积分表示结果。我们的分析基于在Bouchittè，Fonseca，Leoni和Mascarenhas（2002）中设计的全球放松方法的可变指数版本，用于恒定指数。我们证明了相同类型能量序列的$γ$ - 通过渐近细胞公式识别限制的积分，并证明了大块和表面贡献之间的非相互作用。
An integral representation result for free-discontinuity energies defined on the space $GSBV^{p(\cdot)}$ of generalized special functions of bounded variation with variable exponent is proved, under the assumption of log-Hölder continuity for the variable exponent $p(x)$. Our analysis is based on a variable exponent version of the global method for relaxation devised in Bouchittè, Fonseca, Leoni and Mascarenhas (2002) for a constant exponent. We prove $Γ$-convergence of sequences of energies of the same type, we identify the limit integrands in terms of asymptotic cell formulas and prove a non-interaction property between bulk and surface contributions.
