Abstract
For arbitrary generalized solutions of parabolic impulse control problems, a local estimate of the Hölder norms is obtained. The boundedness of the Hölder norms of solutions subject to the Neumann boundary condition is proved. The results are established under the same hypotheses as in the classical problems. Bibliography: 4 titles.
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Literature Cited
O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva,Linear and Quasilinear Equations of Parabolic Type, American Mathematical Society, Providence (1968).
M. Biroli, “Hölder continuity for parabolic obstacle problem,”Boll. Unione. Mat. Ital., VII. Ser. B,6, No. 1, 1079–1088 (1982).
Additional information
Translated fromProblemy Matematicheskogo Analiza, No. 14, 1995, pp. 122–142.
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Tregub, V.L. On the Hölder regularity for parabolic quasivariational inequalities of impulse control. J Math Sci 77, 3346–3361 (1995). https://doi.org/10.1007/BF02364866
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DOI: https://doi.org/10.1007/BF02364866