Regular Article
Parabolic Problems with Nonlinear Boundary Conditions and Critical Nonlinearities

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Abstract

We prove existence, uniqueness and regularity of solutions for heat equations with nonlinear boundary conditions. We study these problems with initial data in Lq(Ω), W1, q(Ω), 1<q<∞ or measures and with critically growing nonlinearities.

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Partially supported by DGICYT, PB96-0648, Spain.

Partially supported by CNPq, Ministry of Science and Technology, Brazil, Grant 300.889/92-5, and a sabatical position from UCM.

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E-mail: [email protected]

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E-mail: [email protected]

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E-mail: [email protected]