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Dont, Miroslav
A note on the parabolic variation. (English). Mathematica Bohemica, vol. 125 (2000), issue 3, pp. 257-268
MSC: 31A20, 31A25, 35K05 | MR 1790119 | Zbl 0965.31001 | DOI: 10.21136/MB.2000.126129
Keywords:
boundary value problem for the heat equation; integral equation; heat equation; boundary value problem; parabolic variation
Summary:
A condition for solvability of an integral equation which is connected with the first boundary value problem for the heat equation is investigated. It is shown that if this condition is fulfilled then the boundary considered is $\frac12$-Holder. Further, some simple concrete examples are examined.
References:
[1] M. Dont: Fourier problem with bounded Baire data. Math. Bohem. 22 (1997), 405-441. MR 1489402 | Zbl 0898.31004
[2] M. Dont: On a heat potential. Czechoslovak Math. J. 25 (1975), 84-109. MR 0369918 | Zbl 0304.35051
[3] M. Dont: A note on a heat potential and the parabolic variation. Čas. Pӗst. Mat. 101 (1976), 28-44. MR 0473536 | Zbl 0325.35043
[4] J. Král: Teorie potenciálu I. SPN, Praha, 1965.
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