Quasilinear riccati type equations with super-critical exponents

Document Type

Article

Publication Date

10-20-2010

Abstract

We establish explicit criteria of solvability for the quasilinear Riccati type equation -Δpu = {pipe}∇u{pipe}q + ω in a bounded C{script}1 domain Ω⊂ℝn, n ≥ 2. Here Δp, p > 1, is the p-Laplacian, q is in the supper critical range q > p, and the datum ω is a measure. Our existence criteria are given in the form of potential theoretic or geometric estimates that are sharp when ω is nonnegative and compactly supported in Ω. Our existence results are new even in the case dω = f dx where f belongs to the weak Lebesgue space L n(q-p+1)/q,∞ (Ω). Moreover, our methods allow the treatment of more general equations where the principal operators may have discontinuous coefficients. As a consequence of the solvability results, a characterization of removable singularities for the corresponding homogeneous equation is also obtained. © Taylor & Francis Group, LLC.

Publication Source (Journal or Book title)

Communications in Partial Differential Equations

First Page

1958

Last Page

1981

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