论文标题
带有可变指数的双相问题的新嵌入结果和相应的广义双相问题的先验界限
New embedding results for double phase problems with variable exponents and a priori bounds for corresponding generalized double phase problems
论文作者
论文摘要
在本文中，我们介绍了双相型的Musielak-Orlicz Sobolev空间的新嵌入结果。基于$ w^{1，\ Mathcal {h}}}（ω）$的连续嵌入到$ l^{\ Mathcal {h} _*}（ω）$中，其中$ \ nathcal {h} _*$是sobolev conjugate conjugate conjugate conjugate of $ \ natercal nefore norders norders stront stront stront strort as intrant stront astry astry at intrestions tornation intrant intrant intrant intrant intrant and stront astrection。基于这些结果，我们考虑了涉及Dirichlet和非线性边界条件的这种新型增长类型的广义双相问题，并证明了基于DE Giorgi迭代的相应弱解决方案以及本地化参数的适当界限结果。
In this paper we present new embedding results for Musielak-Orlicz Sobolev spaces of double phase type. Based on the continuous embedding of $W^{1,\mathcal{H}}(Ω)$ into $L^{\mathcal{H}_*}(Ω)$, where $\mathcal{H}_*$ is the Sobolev conjugate function of $\mathcal{H}$, we present much stronger embeddings as known in the literature. Based on these results, we consider generalized double phase problems involving such new type of growth with Dirichlet and nonlinear boundary condition and prove appropriate boundedness results of corresponding weak solutions based on the De Giorgi iteration along with localization arguments.
