Strong Solvability of a Unilateral Boundary Value Problem for Nonlinear Parabolic Operators |
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Authors: | Rosalba Di Vincenzo |
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Institution: | (1) Department of Mathematics and Computer Sciences, University of Catania, Viale A. Doria, 6, 95125 Catania, Italy |
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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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Keywords: | Primary 35K60 Secondary 35K85 |
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