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Intermediate Schauder estimates for oblique derivative problems. (English) Zbl 0603.35025
From the author’s introduction: The author extends the intermediate Schauder estimates of Gilbarg and Hörmander for the Dirichlet problem \[ Pu=f\quad in\quad \Omega,\quad u=u_ 0\quad on\quad \partial \Omega \] to the regular oblique derivative problem \[ Pu=f\quad in\quad \Omega,\quad Mu=g\quad on\quad \partial \Omega, \] where P is a second order elliptic operator and M is a first order regular oblique differential operator.
Reviewer: N.Maria

MSC:
35J25 Boundary value problems for second-order elliptic equations
35B45 A priori estimates in context of PDEs
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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References:
[1] D. Gilbarg & L. Hörmander, Intermediate Schauder estimates, Arch. Rational Mech. Anal. 74 (1980), 297-318. · Zbl 0454.35022
[2] D. Gilbaro & N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin-Heidelberg-New York, 1977. 2nd ed. 1983.
[3] L. Hörmander, The boundary problems of physical geodesy, Arch. Rational Mech. Anal. 62 (1976), 1-52. · Zbl 0331.35020
[4] G. M. Lieberman, Solvability of quasilinear elliptic equations with nonlinear boundary conditions, Trans. Am. Math. Soc. 273 (1982), 753-765. · Zbl 0498.35039
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