The solvability of the Dirichlet problem for quasilinear elliptic second-order equations of nondivergence form is studied in weight spaces. Bibliography: 10 titles.
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A. I. Nazarov, “Estimates for the maximumof solutions of elliptic and parabolic equations in terms of weighted norms of the right-hand side,” Algebra Analiz, 13, No. 2, 151-164 (2001).
D.E. Apushkinskaya and A. I. Nazarov, “The Dirichlet problem for quasilinear elliptic equations in domains with smooth closed edges,” Probl. Mat. Anal., No. 21, 3-29 (2000).
O.A. Ladyzhenskaya and N.N. Uraltseva, “Estimates of max |u x| for solutions of quasilinear elliptic and parabolic equations of general type and some existence theorems,” Zap. Nauchn. Semin. LOMI, 138, 90-107 (1984).
D. E. Apushkinskaya and A. I. Nazarov, “Boundary estimates for the first-order derivatives of a solution to a nondivergent parabolic equation with composite right-hand side and coeficients of lower-order derivatives,” Probl. Mat. Anal., No. 14, 3-27 (1995).
D. E. Apushkinskaya and A. I. Nazarov, “The initial boundary-value problem for nondivergent parabolic equations with Venttsel' boundary condition,” Algebra Analiz, 6, No. 6, 1-29.
O.V. Besov, V.P. Il'in, and S.M. Nikol'skii, Integral Representations of Functions and Embedding Theorems [in Russian], Moscow (1996).
A. I. Nazarov, “L p-estimates for a solution to the Dirichlet problem and to the Neumann problem for the heat equation in a wedge with edge of arbitrary codimension,” Probl. Mat. Anal., No. 22, 126-159 (2001).
O. A. Ladyzhenskaya and N. N. Uraltseva, Linear and Quasilinear Elliptic Equations [in Russian], Moscow (1973).
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Apushkinskaya, D.E., Nazarov, A.I. The Dirichlet Problem in Weight Spaces. Journal of Mathematical Sciences 123, 4527–4538 (2004). https://doi.org/10.1023/B:JOTH.0000041472.40491.f1
- Dirichlet Problem
- Weight Space
- Nondivergence Form