Hopf type lemmas for subsolutions of integro-differential equations
نویسندگان
چکیده
In the paper we prove a lower bound for subsolutions of integro-differential equation: −Au+cu=0 in domain D. It states that there exists Borel function ψ, strictly positive on D, depending only coefficients operator A, c and D such any subsolution u(⋅), satisfies supy∈DSu(y)≥0, one can find constant a>0 (that general depends u), which supy∈DSu(y)−u(x)≥aψ(x), x∈D. The is valid wide class Lévy type operators non-negative, bounded measurable quite D⊂Rd. Here DS certain set containing closure determined by support Levy jump measure associated with A. some cases non-negative eigenfunction corresponding to be admitted as ψ. particular, this occurs when transition probability semigroup A ultracontractive. main assumptions made about are: strong Markov solution martingale problem its resolvent minorization condition. This result call generalized Hopf lemma.
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ژورنال
عنوان ژورنال: Bernoulli
سال: 2023
ISSN: ['1573-9759', '1350-7265']
DOI: https://doi.org/10.3150/22-bej1505