We consider the partial differential equation u−f=div(u^m ∇u/|∇u|) with f nonnegative and bounded and m∈R. We prove existence and uniqueness of solutions for both the Dirichlet problem (with bounded and nonnegative boundary datum) and the homogeneous Neumann problem. Solutions, which a priori belong to a space of truncated bounded variation functions, are shown to have zero jump part with respect to the ℋ^{N−1}-Hausdorff measure. Results and proofs extend to more general nonlinearities.

Nonlinear diffusion in transparent media: the resolvent equation / Giacomelli, Lorenzo; Salvador, Moll; Petitta, Francesco. - In: ADVANCES IN CALCULUS OF VARIATIONS. - ISSN 1864-8266. - STAMPA. - 11:4(2018), pp. 405-432. [10.1515/acv-2017-0002]

Nonlinear diffusion in transparent media: the resolvent equation

GIACOMELLI, Lorenzo;PETITTA, FRANCESCO
2018

Abstract

We consider the partial differential equation u−f=div(u^m ∇u/|∇u|) with f nonnegative and bounded and m∈R. We prove existence and uniqueness of solutions for both the Dirichlet problem (with bounded and nonnegative boundary datum) and the homogeneous Neumann problem. Solutions, which a priori belong to a space of truncated bounded variation functions, are shown to have zero jump part with respect to the ℋ^{N−1}-Hausdorff measure. Results and proofs extend to more general nonlinearities.
2018
Total variation; transparent media; linear growth Lagrangian; comparison principle; Dirichlet problems; Neumann problems
01 Pubblicazione su rivista::01a Articolo in rivista
Nonlinear diffusion in transparent media: the resolvent equation / Giacomelli, Lorenzo; Salvador, Moll; Petitta, Francesco. - In: ADVANCES IN CALCULUS OF VARIATIONS. - ISSN 1864-8266. - STAMPA. - 11:4(2018), pp. 405-432. [10.1515/acv-2017-0002]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1010720
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