In this paper we prove existence, uniqueness, and regularity results for solutions of nonlinear elliptic equations in which the differential operator has logarithmic growth with respect to the gradient. The solution will belong to the Sobolev space W1,1 0 (Ω), to the Orlicz–Sobolev space generated by the function tlog(1 + |t|), but not to any Sobolev space W1,p 0 (Ω), with p > 1.
Leray–Lions operators with logarithmic growth / Boccardo, Lucio; Orsina, Luigi. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 423:(2015), pp. 608-622. [10.1016/j.jmaa.2014.09.065]
Leray–Lions operators with logarithmic growth
BOCCARDO, Lucio;ORSINA, Luigi
2015
Abstract
In this paper we prove existence, uniqueness, and regularity results for solutions of nonlinear elliptic equations in which the differential operator has logarithmic growth with respect to the gradient. The solution will belong to the Sobolev space W1,1 0 (Ω), to the Orlicz–Sobolev space generated by the function tlog(1 + |t|), but not to any Sobolev space W1,p 0 (Ω), with p > 1.File allegati a questo prodotto
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