A priori estimates for gradients of solutions of a boundary-value problem for a quasilinear nondivergent elliptic equation with the quasilinear Ventzel boundary condition are established. By these estimates, existence theorems in the Hölder and Sobolev spaces are proved. Bibliography:11 titles.
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Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 221, 1995, pp. 20–29.
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Apushkinskaya, D.E., Nazarov, A.I. On the quasilinear stationary Ventzel boundary-value problem. J Math Sci 87, 3277–3283 (1997). https://doi.org/10.1007/BF02355580
- Boundary Condition
- Sobolev Space
- Elliptic Equation
- Existence Theorem
- Nondivergent Elliptic Equation