Abstract
We study in this paper a class of second-order linear elliptic equations in weighted Sobolev spaces on unbounded domains of , . We obtain an a priori bound, and a regularity result from which we deduce a uniqueness theorem.
Highlights
Let Ω be an open subset of Rn, n ≥ 3
It is well known that if Ω is a bounded and sufficiently regular set, the above problem has been widely investigated by several authors under various hypotheses of discontinuity on the leading coefficients, in the case p 2 or p sufficiently close to 2
International Journal of Mathematics and Mathematical Sciences proved in 1, where the author assumed that aij ’s belong to W1,n Ω and considered the case p 2 and in 2–4 where the coefficients belong to some classes wider than W1,n Ω
Summary
Let Ω be an open subset of Rn, n ≥ 3. It is well known that if Ω is a bounded and sufficiently regular set, the above problem has been widely investigated by several authors under various hypotheses of discontinuity on the leading coefficients, in the case p 2 or p sufficiently close to 2. Some W2,p-bounds for the solutions of the problem 1.2 and related existence and uniqueness results have been obtained. International Journal of Mathematics and Mathematical Sciences proved in 1 , where the author assumed that aij ’s belong to W1,n Ω and considered the case p 2 and in 2–4 where the coefficients belong to some classes wider than W1,n Ω. A similar weighted case was studied in 15 with the leading coefficients satisfying hypotheses of Miranda’s type and when p 2
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