McOwen, Robert C. The behavior of the Laplacian on weighted Sobolev spaces. (English) Zbl 0426.35029 Commun. Pure Appl. Math. 32, 783-795 (1979). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 80 Documents MSC: 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 47A53 (Semi-) Fredholm operators; index theories Keywords:Laplace operator; weighted Sobolev spaces; Fredholm operator PDF BibTeX XML Cite \textit{R. C. McOwen}, Commun. Pure Appl. Math. 32, 783--795 (1979; Zbl 0426.35029) Full Text: DOI OpenURL References: [1] , and , Partial Differential Equations, Wiley, New York, 1964. [2] Cantor, Indiana Univ. Math. J. 24 pp 897– (1975) [3] On the index of elliptic partial differential operators in Rn, preprint. [4] Foundations of Potential Theory, Springer-Verlag, Berlin, 1929. · JFM 55.0282.01 [5] Nirenberg, J. Math. Anal. Appl. 42 pp 271– (1973) [6] and , Methods of Modern Mathematical Physics, Vol. II, Academic Press, New York, 1975. [7] and , Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, 1971. · Zbl 0232.42007 [8] Basic Linear Partial Differential Equations, Academic Press, New York, 1975. · Zbl 0305.35001 [9] Stein, J. Math. Mech. 7 pp 503– (1958) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.