Spaces with homogeneous norms
1980 ◽
Vol 21
(2)
◽
pp. 189-205
◽
Keyword(s):
Spaces with homogeneous norms are closely related to the Beppo Levi spaces of Deny and Lions, to spaces of Riesz potentials, and to Sobolev spaces. In this paper we survey the literature on them, give a broad extension of their definition, and present their basic theory. Many of the properties of Sobolev spaces have their analogues. In fact, the two families are locally equivalent. Spaces with homogeneous norms are especially suited to the study of boundary value problems on for homogeneous elliptic operators with constant coefficients. We will use them extensively in a forthcoming paper to study elliptic partial differential equations with mixed boundary conditions on a smoothly bounded domain.
1976 ◽
Vol 15
(3)
◽
pp. 475-476
◽
1981 ◽
Vol 90
(3-4)
◽
pp. 347-359
◽
2006 ◽
Vol 254
(1)
◽
pp. 33-54
◽
2018 ◽
pp. 10-14
1985 ◽
Vol 100
(3-4)
◽
pp. 219-235
◽
2014 ◽
Vol 21
(1)
◽
pp. 95-146
◽
2018 ◽
Vol 65
◽
pp. 231-247
◽
2005 ◽
Vol 07
(06)
◽
pp. 787-808
2010 ◽
Vol 172
(3)
◽
pp. 347-400
◽