Second derivative $L^ p$-estimates for elliptic equations of nondivergent type
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- by Fang-Hua Lin PDF
- Proc. Amer. Math. Soc. 96 (1986), 447-451 Request permission
Abstract:
We obtain an a priori estimate of second derivatives in ${L^p}$, for some $p > 0$, for solutions of nondivergent, uniformly elliptic P.D.E.’s of second order.References
- R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241–250. MR 358205, DOI 10.4064/sm-51-3-241-250 L. C. Evans, Some estimates for non-divergence structure, second order elliptic equations, preprint. E. B. Fabes and D. W. Stroock, The ${L^p}$-integrability of Green’s functions and fundamental solutions for elliptic and parabolic equations, IMA preprint #47, Univ. of Minnesota, 1983.
- Carlo Pucci and Giorgio Talenti, Elliptic (second-order) partial differential equations with measurable coefficients and approximating integral equations, Advances in Math. 19 (1976), no. 1, 48–105. MR 419989, DOI 10.1016/0001-8708(76)90022-0
- David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, Grundlehren der Mathematischen Wissenschaften, Vol. 224, Springer-Verlag, Berlin-New York, 1977. MR 0473443, DOI 10.1007/978-3-642-96379-7 N. N. Ural’tseva, Impossibility of $W_q^2$-bounds for multi-dimensional elliptic equations with discontinuous coefficients, Sem. Leningrad Otdel Mat. Inst. Steklov 5 (1967). (Russian)
- Carlo Pucci, Limitazioni per soluzioni di equazioni ellittiche, Ann. Mat. Pura Appl. (4) 74 (1966), 15–30 (Italian, with English summary). MR 214905, DOI 10.1007/BF02416445
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 447-451
- MSC: Primary 35J15; Secondary 35B45
- DOI: https://doi.org/10.1090/S0002-9939-1986-0822437-1
- MathSciNet review: 822437