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Strong Solvability of a Unilateral Boundary Value Problem for Nonlinear Parabolic Operators

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Abstract.

Strong solvability in Sobolev spaces is proved for a unilateral boundary value problem for nonlinear parabolic operators. The operator is assumed to be of Carathéodory type and to satisfy a suitable ellipticity condition; only measurability with respect to the independent variable X is required.

The main tools of the proof are an estimate for the second derivatives of functions which satisfy the unilateral boundary conditions and the monotonicity of the operator − u t with respect to Δu for the same functions.

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Authors and Affiliations

  1. Department of Mathematics and Computer Sciences, University of Catania, Viale A. Doria, 6, 95125, Catania, Italy

    Rosalba Di Vincenzo

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  1. Rosalba Di Vincenzo
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Correspondence to Rosalba Di Vincenzo.

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Di Vincenzo, R. Strong Solvability of a Unilateral Boundary Value Problem for Nonlinear Parabolic Operators. MedJM 4, 119–126 (2007). https://doi.org/10.1007/s00009-007-0107-0

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  • DOI: https://doi.org/10.1007/s00009-007-0107-0

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