Differentiability of solutions of some unilateral problem of parabolic type

Hiroki TANABE

doi:10.2969/jmsj/03330367

Hiroki TANABE

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JOURNAL FREE ACCESS

1981 Volume 33 Issue 3 Pages 367-403

DOI https://doi.org/10.2969/jmsj/03330367

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Published: 1981 Received: June 04, 1979 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Right : [1] H. Brézis, Opérateurs maximaux monotones et semigroupes de contractions dans les espaces Hilbert, Math. Studies, North Holland Math. Studies, 5, North-Holland, Amsterdam, 1973.
[2] H. Brézis, Problémes unilatéraux, J. Math. Pures Appl., 51 (1972), 1-168.
[3] F. E. Browder, On the spectral theory of elliptic differential operators I, Math. Ann., 142 (1961), 22-130.
[4] F. E. Browder, Nonlinear maximal monotone operators in Banach space, Math. Ann., 175 (1968), 89-113.
[5] B. D. Calvert and C. P. Gupta, Nonlinear elliptic boundary value problems in L^p-spaces and sums of ranges of accretive operators, Nonlinear Anal., 2 (1978), 1-26.
[6] M. G. Crandall and T. M. Liggett, Generation of semi-groups of nonlinear transformations on general Banach spaces, Amer. J. Math., 93 (1971), 265-298.
[7] M. G. Crandall and A. Pazy, Nonlinear evolution equations in Banach spaces, Israel J. Math., 11 (1972), 56-94.
[8] L. C. Evans, Differentiability of a nonlinear semigroup in L¹, J. Math. Anal. Appl., 60 (1977), 703-715.
[9] L. C. Evans, Regularity properties for the heat equation subject to nonlinear boundary constraints, Nonlinear Anal., 1 (1977), 593-602.
[10] N. Kerzman, Hölder and L^p estimates for solutions of ∂u=f in strongly pseudoconvex domains, Comm. Pure Appl. Math., 24 (1971), 289-300.
[11] F. J. Massey, III, Semilinear parabolic equations with L¹ initial data, Indiana Univ. Math. J., 26 (1977), 399-412.
[12] H. Tanabe, On Green's functions of elliptic and parabolic boundary value problems, Proc. Japan Acad., 48 (1972), 709-711.
[13] H. Tanabe, On some unilateral problem of elliptic and parabolic type, Proc. Japan Acad., 54 A (1978), 194-196.
[14] H. Tanabe, Remarks on the differentiability of solutions of some semilinear parabolic equations, Proc. Japan Acad., 54 A (1978), 314-317.

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