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Nonlinear parabolic equations with natural growth in general domains

A. Dall'aglioD. GiachettiJ.-P. Puel — 2005

Bollettino dell'Unione Matematica Italiana

We prove an existence result for a class of parabolic problems whose principal part is the p -Laplace operator or a more general Leray-Lions type operator, and featuring an additional first order term which grows like | u | p . Here the spatial domain can have infinite measure, and the data may be not regular enough to ensure the boundedness of solutions. As a consequence, solutions are obtained in a class of functions with exponential integrability. An existence result of bounded solutions is also given...

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