報告題目：Higher Sobolev regularity on the mixed local and nonlocal p-Laplace equations
報告人：方玉周
邀請人：熊棋
報告時間：2025年5月9日 14:00-15:00
報告地點： 騰訊會議：670-349-390
摘要： In this talk, I will introduce the interior Sobolev regularity of weak solutions to the mixed local and nonlocal p-Laplace equations. To be precise, the weak solution u is shown to belong to W^{2,p} and even W^{2,2} Sobolev spaces in the subquadratic case, while |?u|^{ (p?2)/ 2}?u is of the class W^{1,2} in the superquadratic scenario, both of which coincide with that of the classical p-Laplace equations. Moreover, an improved higher fractional differentiability and integrability result u∈W^{1+β,q} is proved in the full range p∈ (1,∞) for any q∈ [max{p, 2},∞] and β∈ (0, 2/q). This is joint work with Dingding Li and Chao Zhang.
報告人介紹：方玉周，博士畢業(yè)于哈爾濱工業(yè)大學(xué)，現(xiàn)為哈工大kaiyun開云官方網(wǎng)站副研究員。研究興趣主要集中于橢圓和拋物型方程的正則性等理論，研究成果發(fā)表于Math. Ann., Indiana Univ. Math. J., J. Lond. Math. Soc., IMRN等期刊。
