Abstract
We consider the Neumann boundary value problem for the class of (p,q)-nonlinear elliptic equations. The numbers p and q, 2 ⩽ p < q, characterize the power growth with respect to the gradient of eigenvalues of the leading matrix of the equation. An a priori estimate for the maximum of the modulus of the gradient of the solution is obtained in a neighborhood of the boundary of the domain for some interval of p and q. Bibliography: 5 titles.
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References
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I. V. Nezhinskaya, “Boundary estimate for the gradient of a solution to the Dirichlet problem for (p, q)-nonlinear equations” [in Russian], Probl. Mat. Anal., 27 (2004), 137–150; English transl.: J. Math. Sci., 120 (2004), no. 2, 1145–1154.
I. V. Nezhinskaya, “On solvability of the boundary-value problem for (p,q)-nonlinear elliptic and parabolic equations” [in Russian] Probl. Mat. Anal., 29 (2004), 55–69; English transl.: J. Math. Sci., 124 (2004), no. 3, 5001–5017.
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Translated from Problemy Matematicheskogo Analiza, No. 31, 2005, pp. 47–57.
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Nezhinskaya, I.V. Estimate for the Gradient of the Solution to the Neumann Problem for (p,q)-Nonlinear Equations. J Math Sci 132, 428–440 (2006). https://doi.org/10.1007/s10958-005-0509-0
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DOI: https://doi.org/10.1007/s10958-005-0509-0