Comparison principle for unbounded viscosity solutions of degenerate elliptic PDEs with gradient superlinear terms

Abstract : We are concerned with fully nonlinear possibly degenerate elliptic partial differential equations (PDEs) with superlinear terms with respect to $Du$. We prove several comparison principles among viscosity solutions which may be unbounded under some polynomial-type growth conditions. Our main result applies to PDEs with convex superlinear terms but we also obtain some results in nonconvex cases. Applications to monotone systems of PDEs are given.
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Journal of Mathematical Analysis and applications, Elsevier, 2011, 381 (1), pp.110-120. <10.1016/j.jmaa.2011.03.009>
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Shigeaki Koike, Olivier Ley. Comparison principle for unbounded viscosity solutions of degenerate elliptic PDEs with gradient superlinear terms. Journal of Mathematical Analysis and applications, Elsevier, 2011, 381 (1), pp.110-120. <10.1016/j.jmaa.2011.03.009>. <hal-00522569>

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