Boundedness and Hölder continuity of weak solutions of the nonlinear boundary-value problem for elliptic equations with general nonstandard growth conditions
Gumpyong Ri, Dukman Ri
Received November 23, 2023. Published online September 5, 2024.
Abstract: We study a nonlinear boundary-value problem for elliptic equations with critical growth conditions involving Lebesgue measurable functions. We prove global boundedness and Hölder continuity of weak solutions for this problem. Our results generalize the ones obtained by P. Winkert and his colleagues (2012) not only in the variable exponent case but also in the constant exponent case.
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Affiliations: Gumpyong Ri, Dukman Ri (corresponding author), Department of Mathematics, University of Science, Pyongyang, D.P.R. Korea, e-mail: rigumpyong@star-co.net.kp, ridukman@star-co.net.kp