In this paper, we study the Dirichlet problem for an elliptic equation, in which the 1-Laplacian operator and lower-order terms appear. We introduce a suitable definition of solution and prove the existence of, at least, one bounded solution in BV(ohm) having a negligible jump part. Moreover, a uniqueness result for small positive data is proved, and explicit examples of solutions are shown.
Bounded solutions to the 1-Laplacian equation with a critical gradient term / Fuensanta, Andreu; Dall'Aglio, Andrea; Sergio Segura De, Leon. - In: ASYMPTOTIC ANALYSIS. - ISSN 0921-7134. - STAMPA. - 80:1-2(2012), pp. 21-43. [10.3233/asy-2012-1099]
Bounded solutions to the 1-Laplacian equation with a critical gradient term
DALL'AGLIO, Andrea;
2012
Abstract
In this paper, we study the Dirichlet problem for an elliptic equation, in which the 1-Laplacian operator and lower-order terms appear. We introduce a suitable definition of solution and prove the existence of, at least, one bounded solution in BV(ohm) having a negligible jump part. Moreover, a uniqueness result for small positive data is proved, and explicit examples of solutions are shown.File allegati a questo prodotto
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