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Convex semigroups on Lp-like spaces

Author

Listed:
  • Denk, Robert

    (Center for Mathematical Economics, Bielefeld University)

  • Kupper, Michael

    (Center for Mathematical Economics, Bielefeld University)

  • Nendel, Max

    (Center for Mathematical Economics, Bielefeld University)

Abstract

In this paper, we investigate convex semigroups on Banach lattices with order continuous norm, having $L^p$-spaces in mind as a typical application. We show that the basic results from linear $C_0$-semigroup theory extend to the convex case. We prove that the generator of a convex $C_0$-semigroup is closed and uniquely determines the semigroup whenever the domain is dense. Moreover, the domain of the generator is invariant under the semigroup; a result that leads to the well-posedness of the related Cauchy problem. In a last step, we provide conditions for the existence and strong continuity of semigroup envelopes for families of $C_0$-semigroups. The results are discussed in several examples such as semilinear heat equations and nonlinear integro-differential equations.

Suggested Citation

  • Denk, Robert & Kupper, Michael & Nendel, Max, 2025. "Convex semigroups on Lp-like spaces," Center for Mathematical Economics Working Papers 712, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:712
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    File URL: https://pub.uni-bielefeld.de/download/3004630/3004631
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