We obtain existence results for some strongly nonlinear Cauchy problems posed in RN and having merely locally integrable data. The equations we deal with have as principal part a bounded, coercive and pseudo-monotone operator of Leray-Lions type acting on L-p(0, T; W-loc(1,p) (R-N)), they contain absorbing zero order terms and possibly include first order terms with natural growth. For any p > 1 and under optimal growth conditions on the zero order terms, we derive suitable local a-priori estimates and consequent global existence results.

Local estimates and global existence for strongly nonlinear parabolic equations with locally integrable data / Leoni, Fabiana; Benedetta, Pellacci. - In: JOURNAL OF EVOLUTION EQUATIONS. - ISSN 1424-3199. - 6:1(2006), pp. 113-144. [10.1007/s00028-005-0234-7]

Local estimates and global existence for strongly nonlinear parabolic equations with locally integrable data

LEONI, Fabiana;
2006

Abstract

We obtain existence results for some strongly nonlinear Cauchy problems posed in RN and having merely locally integrable data. The equations we deal with have as principal part a bounded, coercive and pseudo-monotone operator of Leray-Lions type acting on L-p(0, T; W-loc(1,p) (R-N)), they contain absorbing zero order terms and possibly include first order terms with natural growth. For any p > 1 and under optimal growth conditions on the zero order terms, we derive suitable local a-priori estimates and consequent global existence results.
2006
absorbing zero order terms; first order terms with natural growth; global existence; l loc 1 data; nonlinear parabolic equations; p-laplacian with p > 1; l-1oc(1) data
01 Pubblicazione su rivista::01a Articolo in rivista
Local estimates and global existence for strongly nonlinear parabolic equations with locally integrable data / Leoni, Fabiana; Benedetta, Pellacci. - In: JOURNAL OF EVOLUTION EQUATIONS. - ISSN 1424-3199. - 6:1(2006), pp. 113-144. [10.1007/s00028-005-0234-7]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/122438
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