Abstract:
One constructs examples of strongly elliptic second-order differential equations in the divergence form with measurable bounded complex coefficients in Rn, n⩾3, whose generalized solutions are not bounded in any neighborhood of the origin.
Citation:
V. G. Maz'ya, S. A. Nazarov, B. A. Plamenevskii, “Absence of De Giorgi-type theorems for strongly elliptic equations with complex coefficients”, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Zap. Nauchn. Sem. LOMI, 115, "Nauka", Leningrad. Otdel., Leningrad, 1982, 156–168; J. Soviet Math., 28:5 (1985), 726–734
\Bibitem{MazNazPla82}
\by V.~G.~Maz'ya, S.~A.~Nazarov, B.~A.~Plamenevskii
\paper Absence of De Giorgi-type theorems for strongly elliptic equations with complex coefficients
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~14
\serial Zap. Nauchn. Sem. LOMI
\yr 1982
\vol 115
\pages 156--168
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl4048}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=660079}
\zmath{https://zbmath.org/?q=an:0498.35033}
\transl
\jour J. Soviet Math.
\yr 1985
\vol 28
\issue 5
\pages 726--734
\crossref{https://doi.org/10.1007/BF02112337}
Linking options:
https://www.mathnet.ru/eng/znsl4048
https://www.mathnet.ru/eng/znsl/v115/p156
This publication is cited in the following 6 articles:
Zhi Dan Wang, Guo Ming Zhang, “A Local Tb Theorem for Square Functions and Parabolic Layer Potentials”, Acta. Math. Sin.-English Ser., 2024
A. F. M. ter Elst, R. Haller-Dintelmann, J. Rehberg, P. Tolksdorf, “On the Lp-theory for second-order elliptic operators in divergence form with complex coefficients”, J. Evol. Equ., 21:4 (2021), 3963
Patrick Tolksdorf, “On off-diagonal decay properties of the generalized Stokes semigroup with bounded measurable coefficients”, J Elliptic Parabol Equ, 7:2 (2021), 323
Wolfgang Arendt, Handbook of Differential Equations: Evolutionary Equations, 1, 2002, 1
E. B. Davies, Partial Differential Equations and Mathematical Physics, 1996, 122
V. G. Maz'ya, S. A. Nazarov, B. A. Plamenevskii, “Elliptic boundary-value problems in domains of the exterior-of-a-cusp type”, J Math Sci, 35:1 (1986), 2227
Citation in format AMSBIB
Contact us: