Weyl’s lemma for pointwise solutions of elliptic equations
HTML articles powered by AMS MathViewer
- by J. R. Diederich PDF
- Proc. Amer. Math. Soc. 37 (1973), 476-480 Request permission
Abstract:
We prove that pointwise, ${L_1}$ solutions of second order elliptic partial differential equations are classical solutions.References
- A.-P. Calderón and A. Zygmund, Local properties of solutions of elliptic partial differential equations, Studia Math. 20 (1961), 171–225. MR 136849, DOI 10.4064/sm-20-2-181-225
- Jim Diederich, Removable sets for pointwise solutions of elliptic partial differential equations, Trans. Amer. Math. Soc. 165 (1972), 333–352. MR 293235, DOI 10.1090/S0002-9947-1972-0293235-X
- James Serrin, On the Harnack inequality for linear elliptic equations, J. Analyse Math. 4 (1955/56), 292–308. MR 81415, DOI 10.1007/BF02787725
- James Serrin, Removable singularities of solutions of elliptic equations, Arch. Rational Mech. Anal. 17 (1964), 67–78. MR 170095, DOI 10.1007/BF00283867
- Victor L. Shapiro, Fourier series in several variables, Bull. Amer. Math. Soc. 70 (1964), 48–93. MR 158222, DOI 10.1090/S0002-9904-1964-11026-0
- Victor L. Shapiro, Removable sets for pointwise solutions of the generalized Cauchy-Riemann equations, Ann. of Math. (2) 92 (1970), 82–101. MR 437898, DOI 10.2307/1970698
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 37 (1973), 476-480
- MSC: Primary 35J30
- DOI: https://doi.org/10.1090/S0002-9939-1973-0318664-3
- MathSciNet review: 0318664