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Examinando Investigación por Materia "1-Laplacian operator"

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    Ítem
    Elliptic 1-Laplacian equations with dynamical boundary conditions
    (2018) Latorre, Marta; Segura de León, Sergio
    This paper is concerned with an evolution problem having an elliptic equation involving the 1-Laplacian operator and a dynamical boundary condition. We apply nonlinear semigroup theory to obtain existence and uniqueness results as well as a comparison principle. Our main theorem shows that the solution we found is actually a strong solution. We also compare solutions with different data.
  • Miniatura
    Ítem
    Existence and comparison results for an elliptic equation involving the 1-Laplacian and L^1-data
    (2018) Latorre, Marta; Segura de León, Sergio
    This paper is devoted to analyse the Dirichlet problem for a nonlinear elliptic equation involving the 1-Laplacian and a total variation term, that is, the inhomogeneous case of the equation arising in the level set formulation of the inverse mean curvature flow. We study this problem in an open bounded set with Lipschitz boundary. We prove an existence result and a comparison principle for non-negative L^1-data. Moreover, we search the summability that the solution reaches when more regular L^p-data, with 1
  • Miniatura
    Ítem
    Existence and uniqueness for the inhomogeneous 1-Laplace evolution equation revisited
    (2022) Latorre, Marta; Segura de León, Sergio
    In this paper we deal with an inhomogeneous parabolic Dirichlet problem involving the 1-Laplacian operator. We show the existence of a unique solution when data belong to L^1(0,T;L^2(\Omega)) for every T>0. As a consequence, global existence and uniqueness for data in L^1_{loc}(0,+\infty;L^2(\Omega)) is obtained. Our analysis retrieves previous results in a correct and complete way.