Compact imbedding of weighted Sobolev space defined on an unbounded domain. II. (English) Zbl 0664.46031

Opic, Bohumir

Čas. Pěstování Mat. 113, No. 3, 293-308 (1988).

The paper deals with the compact imbedding of the weighted Sobolev space \(W_ 0^{k,p}(\Omega,S)\) (S is a collection of weight functions) into the weighted Lebesgue space \(L^ p(\Omega,\rho)\) (\(\rho\) is a weight function). The domain \(\Omega\) is supposed to be unbounded and the above mentioned imbedding is investigated as a limit case of the compact imbeddings of Sobolev spaces defined on bounded domains. Examples are given dealing with power and exponential weights. For part I see ibid. 113, No.1, 60-73 (1988; Zbl 0646.46029).

Reviewer: B.Opic

MSC:

46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46E30	Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords:

unbounded domain; compact imbedding; weighted Sobolev space; weighted Lebesgue space; weight function

Citations:

Zbl 0619.46033; Zbl 0646.46029