Abstract
In [1], Yu. A. Alkhutov and I. T. Mamedov discussed the solvability of the Dirichlet problem for a linear nondivergence uniformly parabolic equations with Cordes coefficients. In this paper, we try to discuss the solvability of initial-mixed boundary value problem for nondivergence uniformly parabolic equations of second order with measurable coefficients in a higher dimensional domain, which includes the Dirichlet problem and initial-oblique derivative problem for the equations as special cases.
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References
Alkhutov Yu. A. and Mamedov I. T., The first boundary value problem for nondivergence second order parabolic equations with discontinuous coefficients. Math. USSR Sbornik 59 (1988), 471–495.
Ladyzhenskaya O. A., Solonnikov V. A. and Ural’ceva N. N., Linear and Quasilinear Equations of Parabolic Type. Trans. Math. Monographs 23, Amer. Math. Soc., Providence, RI, 1968.
Wen G. C. and Begehr H., Boundary Value Problems for Elliptic Equations and Systems. Longman Scientific and Technical, Harlow, 1990.
Wen G. C. and Tain Mao-ying, Initial-oblique derivative problems for nonlinear parabolic equations with measurable coefficients. Comm. in Nonlinear Sci. & Numer. Simu. 2 (1998), 109–113.
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© 2000 Kluwer Academic Publishers
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Wen, G.C. (2000). Initial-Mixed Boundary Value Problems for Parabolic Equations of Second Order with Measurable Coefficients in a Higher Dimensional Domain. In: Begehr, H.G.W., Gilbert, R.P., Kajiwara, J. (eds) Proceedings of the Second ISAAC Congress. International Society for Analysis, Applications and Computation, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0269-8_24
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DOI: https://doi.org/10.1007/978-1-4613-0269-8_24
Publisher Name: Springer, Boston, MA
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