A generalization of a theorem of H. Brezis & F. E. Browder and applications to some unilateral problems
Quasi-linear parabolic equations with degenerate coercivity having a quadratic gradient term
Nonlinear parabolic equations with natural growth in general domains
We prove an existence result for a class of parabolic problems whose principal part is the -Laplace operator or a more general Leray-Lions type operator, and featuring an additional first order term which grows like . 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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