Estimates for solutions to the model Venttsel problem in Campanato spaces
- 46 Downloads
We consider a linear elliptic system of second order equations with constant coefficients in a neighborhood of the plane part of the boundary. The boundary condition contains the conormal derivative and the second order operator containing the tangent derivatives (a Venttsel type problem). For a weak solution we obtain the fundamental Campanato estimates. We clarify the dependence of the smoothness of a weak solution to the corresponding inhomogeneous problem in Campanato spaces on the smoothness of the right-hand sides of the system and boundary conditions. Bibliography: 8 titles.
KeywordsWeak Solution Model Problem Order Derivative Elliptic System Morrey Space
Unable to display preview. Download preview PDF.
- 2.D. A. Apushkinskaya and A. I. Nazrov, “On the quasilinear stationary Venttsel boundary value problem” [in Russian], Zap. Nauchn. Semin. POMI 221, 20–29 (1995); English transl.: J. Math. Sci., New York 87, No. 2, 3277–3283 (1997).Google Scholar
- 3.V. V. Luk’yanov and A. I. Nazarov, “Solving the Venttsel’ problem for the Laplace and Helmholtz equations with the help of iterated potentials” [in Russian], Zap. Nauchn. Semin. POMI 250, 203–218, (1998); English transl.: J. Math. Sci., New York 102, No. 4, 4265–4274 (2000).Google Scholar
- 5.A. A. Arkhipova, Regularity of Weak Solutions to Boundary Value Problems for Linear Equations and Systems of Elliptic Type [in Russian], St. Petersb. State Univ. Press, St. Petersburg (198).Google Scholar