Boundary behavior of large solutions to -Laplacian elliptic equations

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• 作者：Zhijun Zhang ^{chinazjzhang2002@163.com" class="auth_mail" title="E-mail the corresponding author zhangzj@ytu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：pp-Laplacian elliptic equations ; Large solutions ; Boundary behavior
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：33
• 期：Complete
• 页码：40-57
• 全文大小：686 K

文摘

This paper is concerned with exact asymptotic behavior near the boundary of large solutions to quasilinear elliptic equations class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1468121816300402&_mathId=si2.gif&_user=111111111&_pii=S1468121816300402&_rdoc=1&_issn=14681218&md5=893fb13b97be3a79e31c43647b116c40">class="imgLazyJSB inlineImage" height="15" width="181" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S1468121816300402-si2.gif">class="mathContainer hidden">class="mathCode">, where class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1468121816300402&_mathId=si3.gif&_user=111111111&_pii=S1468121816300402&_rdoc=1&_issn=14681218&md5=034f2ba3e9cd5d1048b12053242ef2d1" title="Click to view the MathML source">Ωclass="mathContainer hidden">class="mathCode">$\Omega$ is a bounded smooth domain in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1468121816300402&_mathId=si4.gif&_user=111111111&_pii=S1468121816300402&_rdoc=1&_issn=14681218&md5=183fa908f5b0f419110e23e51b5d07e8" title="Click to view the MathML source">R^Nclass="mathContainer hidden">class="mathCode">${\mathbb{R}}^N$, class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1468121816300402&_mathId=si5.gif&_user=111111111&_pii=S1468121816300402&_rdoc=1&_issn=14681218&md5=4e8b6f1c8a09838a540b3a96a67b4211">class="imgLazyJSB inlineImage" height="17" width="139" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S1468121816300402-si5.gif">class="mathContainer hidden">class="mathCode">${△}_{p}u=\mathrm{div}\left({\left|\nabla u\right|}^{p-2}\nabla u\right)$ with class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1468121816300402&_mathId=si6.gif&_user=111111111&_pii=S1468121816300402&_rdoc=1&_issn=14681218&md5=67f7983de47522b4e8bc97f8ae6ecd31" title="Click to view the MathML source">p>1class="mathContainer hidden">class="mathCode">$p>1$, and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1468121816300402&_mathId=si7.gif&_user=111111111&_pii=S1468121816300402&_rdoc=1&_issn=14681218&md5=d72dcdf376d2460348aab7d4fd38a3ad" title="Click to view the MathML source">b∈C(Ω)class="mathContainer hidden">class="mathCode">$b\in C\left(\Omega \right)$ is nonnegative in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1468121816300402&_mathId=si3.gif&_user=111111111&_pii=S1468121816300402&_rdoc=1&_issn=14681218&md5=034f2ba3e9cd5d1048b12053242ef2d1" title="Click to view the MathML source">Ωclass="mathContainer hidden">class="mathCode">$\Omega$, but may be vanishing or appropriately singular (including critical singular) on the boundary. We give one new condition near infinity on class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1468121816300402&_mathId=si9.gif&_user=111111111&_pii=S1468121816300402&_rdoc=1&_issn=14681218&md5=5961dc14392b50a0ba9f5b7ddd85bfc2" title="Click to view the MathML source">fclass="mathContainer hidden">class="mathCode">$f$ which plays a crucial role in the boundary behavior of solutions.