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Regularity in the two-phase free boundary problems under non-standard growth conditions
Abstracts
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In this paper, we prove several regularity results for the heterogeneous, two-phase free boundary problems $\mathcal {J}_{\gamma}(u)=\int_{\Omega}\big(f(x,\nabla
u)+(\lambda_{+}(u^{+})^{\gamma}+\lambda_{-}(u^{-})^{\gamma})+gu\big)\text{d}x\rightarrow \text{min}$
under non-standard growth conditions. Included in such problems are
heterogeneous jets and cavities of Prandtl-Batchelor type with
$\gamma=0$, chemical reaction problems with $0<\gamma<1$, and obstacle
type problems with $\gamma=1$. Our results hold not only in
the degenerate case of $p> 2$ for $p-$Laplace equations, but
also in the singular
case of $1 |
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From:
Jun Zheng
Subject:
Mathematics
>>
Mathematics （General）
DOI：10.12074/201809.00180
Cite as:
chinaXiv:201809.00180
(or this versionchinaXiv:201809.00180V1)
Recommended references：
Jun Zheng.(2018).Regularity in the two-phase free boundary problems under non-standard growth conditions.[ChinaXiv:201809.00180] (Click&Copy)
| Version History | ||||
|---|---|---|---|---|
| [V1] | 2018-09-22 21:42:36 | chinaXiv:201809.00180V1 | Download | |
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