We prove comparison principles for quasilinear elliptic equations whose simplest model is λu − Du + H(x, Du) = 0 , where Du = div (|Du|p−2Du) is the p-Laplace operator with p > 2, λ ≥ 0, H(x,ξ) : × RN → R is a Carathéodory function and ⊂ RN is a bounded domain, N ≥ 2. We collect several comparison results for weak sub- and super-solutions under different setting of assumptions and with possibly different methods. A strong comparison result is also proved for more regular solutions.
Comparison principles for p-Laplace equations with lower order terms / Leonori, Tommaso; Porretta, Alessio; Riey, Giuseppe. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - (2016), pp. 1-27. [10.1007/s10231-016-0600-9]
Comparison principles for p-Laplace equations with lower order terms
LEONORI, TOMMASO;PORRETTA, Alessio;RIEY, GIUSEPPE
2016
Abstract
We prove comparison principles for quasilinear elliptic equations whose simplest model is λu − Du + H(x, Du) = 0 , where Du = div (|Du|p−2Du) is the p-Laplace operator with p > 2, λ ≥ 0, H(x,ξ) : × RN → R is a Carathéodory function and ⊂ RN is a bounded domain, N ≥ 2. We collect several comparison results for weak sub- and super-solutions under different setting of assumptions and with possibly different methods. A strong comparison result is also proved for more regular solutions.| File | Dimensione | Formato | |
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