Glasnik Matematicki, Vol. 54, No. 1 (2019), 211-232.

MULTIVALUED ANISOTROPIC PROBLEM WITH FOURIER BOUNDARY CONDITION INVOLVING DIFFUSE RADON MEASURE DATA AND VARIABLE EXPONENTS

Ibrahime Konaté and Stanislas Ouaro

Laboratoire de Mathématiques et Informatique, UFR. Sciences Exactes et Appliquées, Université Joseph Ki Zerbo, 03 BP 7021 Ouaga 03, Ouagadougou, Burkina Faso
e-mail: ibrakonat@yahoo.fr
e-mail: ouaro@yahoo.fr


Abstract.   We study a nonlinear anisotropic elliptic problem under Fourier type boundary condition governed by a general anisotropic operator with variable exponents and diffuse Radon measure data which does not charge the sets of zero p(·)-capacity. We prove an existence and uniqueness result of entropy or renormalized solution.

2010 Mathematics Subject Classification.   35J60, 35J65, 35J20, 35J25

Key words and phrases.   Fourier boundary, generalized Lebesgue-Sobolev spaces, anisotropic Sobolev spaces, weak solution, entropy solution, maximal monotone graph, bounded Radon diffuse measure, Marcinkiewicz spaces


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DOI: 10.3336/gm.54.1.09


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