We prove a comparison principle for unbounded weak sub/super solutions of the equation λu − div(A(x)Du) = H(x, Du) in Ω where A(x) is a bounded coercive matrix with measurable ingredients, λ ≥ 0 and ξ → H(x, ξ) has a super linear growth and is convex at infinity. We improve earlier results where the convexity of H(x, ·) was required to hold globally.
On the comparison principle for unbounded solutions of elliptic equations with first order terms / Leonori, Tommaso; Porretta, Alessio. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 457:(2018), pp. 1492-1501. [10.1016/j.jmaa.2017.04.018]
On the comparison principle for unbounded solutions of elliptic equations with first order terms
LEONORI, TOMMASO;PORRETTA, Alessio
2018
Abstract
We prove a comparison principle for unbounded weak sub/super solutions of the equation λu − div(A(x)Du) = H(x, Du) in Ω where A(x) is a bounded coercive matrix with measurable ingredients, λ ≥ 0 and ξ → H(x, ξ) has a super linear growth and is convex at infinity. We improve earlier results where the convexity of H(x, ·) was required to hold globally.| File | Dimensione | Formato | |
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