Monotonicity for elliptic equations in unbounded Lipschitz domains

Berestycki, H.; Caffarelli, Luis A.; Nirenberg, Louis

doi:10.1002/(sici)1097-0312(199711)50:11<1089::aid-cpa2>3.0.co;2-6

Cited by 230 publications

(282 citation statements)

References 12 publications

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“…We first recall two lemmas. The first one is from [BHM] which is a simple consequence of Lemma 2.1 in [BCN1]. …”

Section: Odd Nonlinearity and Related Resultsmentioning

confidence: 99%

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Some remarks related to De Giorgi’s conjecture

2002

Proc. Amer. Math. Soc.

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“…We first recall two lemmas. The first one is from [BHM] which is a simple consequence of Lemma 2.1 in [BCN1]. …”

Section: Odd Nonlinearity and Related Resultsmentioning

confidence: 99%

“…One of the main results in these papers says that if u solves (1.1) and satisfies |u| ≤ 1 and F1] further observes that, under the restrictions already put on the nonlinearity, a result in [BCN1] implies that (1.2) is equivalent to…”

Section: Introductionmentioning

confidence: 99%

Some remarks related to De Giorgi’s conjecture

2002

Proc. Amer. Math. Soc.

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“…The proof in [10] of such a maximum principle simply uses a comparison function similar to the one used in the beginning of Section 2.4.…”

Section: Below)mentioning

confidence: 99%

Layer solutions in a half‐space for boundary reactions

Cabré

Solà-Morales

2005

Comm Pure Appl Math

247

362

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“…This may be regarded as a result for half-space problems already studied in [5]. Our method here for dimensions n = 4, 5 gives a completely different approach from those in [5]. We hope to use this special case to illustrate the strength as well as the limitation of this approach.…”

Section: Comments and Remarksmentioning

confidence: 95%