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green's function estimates

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Combined effects in mixed local–nonlocal stationary problems
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Rakesh Arora, Vicenţiu D. Rădulescu
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View

Published online by Cambridge University Press:

04 September 2023, pp. 1-47
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In this work, we study an elliptic problem involving an operator of mixed order with both local and nonlocal aspects, and in either the presence or the absence of a singular nonlinearity. We investigate existence or nonexistence properties, power- and exponential-type Sobolev regularity results, and the boundary behaviour of the weak solution, in the light of the interplay between the summability of the datum and the power exponent in singular nonlinearities.