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Summability of the Solutions to Nonlinear Parabolic Equations with Measure Data

Feng-Quan Li Guang-Wei Li

2000 · Journal of Convex Analysis · 1 citation · 2 references

Abstract

<jats:p> The authors improve the <jats:inline-formula> <jats:alternatives> <jats:tex-math notation="LaTeX">L^p</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> estimates from the earlier papers of L. Boccardo, T. Gallouet, J. M. Rakotoson, et al., for weak solutions in <jats:inline-formula> <jats:alternatives> <jats:tex-math notation="LaTeX">L^1(0, T; W_0^{1,1}(\Omega))</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>1</mml:mn> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mn>0</mml:mn> <mml:mo separator="true">,</mml:mo> <mml:mi>T</mml:mi> <mml:mo separator="true">;</mml:mo> <mml:msubsup> <mml:mi>W</mml:mi> <mml:mn>0</mml:mn> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo separator="true">,</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="normal">Ω</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> to nonlinear parabolic equations with right hand side and initial value involving measure data.We give an improvement of the summability of solutions to nonlinear parabolic equations with measure data. </jats:p>

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