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- W1991454393 abstract "In particular our chief concern will be with the differentiability properties of generalized solutions of (1.1) in the neighborhood of a point on an arc across which the coefficients of (1.1) have finite jump discontinuities. A well-known local result [1], [5] may be stated as follows: If the coefficients of (1.1) are Holder continuous in G, the closure of a disk G with center at a point to, then there exists a closed disk G1 with center at to and G1CG such that the first derivatives of any generalized solution(2) w(z) of (1.1) in G are H6lder continuous in U1. Suppose now that G is separated into two parts G+ and Gby a sufficiently simple arc L passing through to, and that the coefficients A(z), B(z), C(z), and D(z) are Holder continuous in each of the closed regions G+ and Gand therefore have at most finite jump discontinuities across L. In Theorem 1, it is shown that there exists a suitably chosen disk Go with center at to and GoCG, such that the first derivatives w, and wd of any generalized solution of (1.1) are Holder continuous in each of the two closed regions Go+ and Go separately. This says that the derivatives w, and w2 are smooth up to L in Go from either side of L and have at most finite jump discontinuities across it. In ?4 we specialize (1.1) to Beltrami's equation" @default.
- W1991454393 created "2016-06-24" @default.
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- W1991454393 date "1966-01-01" @default.
- W1991454393 modified "2023-10-17" @default.
- W1991454393 title "On the differentiability of generalized solutions of first order elliptic equations with discontinuous coefficients" @default.
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- W1991454393 doi "https://doi.org/10.1090/s0002-9947-1966-0201805-7" @default.
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