Abstract
A Dirichlet problem for a second-order nonlinear elliptic equation in the general divergent form with a right-hand side from L 1 is considered. The high-order coefficients in the equation are assumed to satisfy the degenerate coercivity condition. The main results concern a priori properties of summability and some estimates of entropy solutions of this problem.
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 16, Differential and Functional Differential Equations. Part 2, 2006.
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Kovalevsky, A.A. A priori properties of solutions of nonlinear equations with degenerate coercivity and L 1-data. J Math Sci 149, 1517–1538 (2008). https://doi.org/10.1007/s10958-008-0080-6
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DOI: https://doi.org/10.1007/s10958-008-0080-6