论文标题
关于强烈非均匀性$ P，Q $分类问题和应用的全球规律性结果的注释
A note on the global regularity results for strongly nonhomogeneous $p,q$-fractional problems and applications
论文作者
论文摘要
在本文中，我们瞥见了全球规律性结果的证据，以解决一类涉及分数$（p，q）$ - laplacian的问题，由$（ - δ）^{s_1} _ {p} _ {p} _ {p}+（ - δ）+（ - δ） $ 1 <p，q <\ infty $。我们还为涉及最关键生长非线性的相应问题的弱解决方案获得了边界Hölder的连续性结果。这些结果几乎是最佳的。此外，我们建立了HOPF类型的最大原则和强大的比较原则。作为对这些新结果的应用，我们证明了Sobolev与Hölder最小化型结果，该结果以精确的工作精神\ cite {brezis-nirenberg}提供了多种解决方案。
In this article, we communicate with the glimpse of the proofs of global regularity results for weak solutions to a class of problems involving fractional $(p,q)$-Laplacian, denoted by $(-Δ)^{s_1}_{p}+(-Δ)^{s_2}_{q}$, for $s_2, s_1\in (0,1)$ and $1<p,q<\infty$. We also obtain the boundary Hölder continuity results for the weak solutions to the corresponding problems involving at most critical growth nonlinearities. These results are almost optimal. Moreover, we establish Hopf type maximum principle and strong comparison principle. As an application to these new results, we prove the Sobolev versus Hölder minimizer type result, which provides the multiplicity of solutions in the spirit of seminal work \cite{Brezis-Nirenberg}.
