Hölder continuity and higher integrability results of weak solutions of the nonlinear boundary-value problem for double phase equations involving variable exponents
Dukman RI, Ryongjin HAN
Received July 22, 2025. Published online May 29, 2026.
Abstract: We study a nonlinear boundary-value problem for double phase elliptic equations involving variable exponents. We first prove boundedness and Hölder continuity of weak solutions for this problem, and then establish higher integrability of gradients of weak solutions by using the Hölder continuity results. Our results partially generalize those obtained by Winkert and others.
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Affiliations: Dukman Ri (corresponding author), Ryongjin Han, Department of Mathematics, University of Science, Pyongyang, Democratic People's Republic of Korea, e-mail: ridukman@star-co.net.kp