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Combined effects in mixed local–nonlocal stationary problems

Part of: Miscellaneous topics - Partial differential equations Elliptic equations and systems Integral, integro-differential, and pseudodifferential operators Partial differential equations

Published online by Cambridge University Press:  04 September 2023

Rakesh Arora  and
Vicenţiu D. Rădulescu Open the ORCID record for Vicenţiu D. Rădulescu [Opens in a new window]
Rakesh Arora
Affiliation:
Department of Mathematical Sciences, Indian Institute of Technology Varanasi (IIT-BHU), Uttar Pradesh 221005, India (rakesh.mat@iitbhu.ac.in, arora.npde@gmail.com)
Vicenţiu D. Rădulescu
Affiliation:
Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 3058/10, Brno 61600, Czech Republic Simion Stoilow Institute of Mathematics of the Romanian Academy, Calea Griviţei 21, 010702 Bucharest, Romania School of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China Department of Mathematics, University of Craiova, Street A.I. Cuza 13, 200585 Craiova, Romania (radulescu@inf.ucv.ro)
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Abstract

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.

Keywords

existence resultspower- and exponential-type Sobolev regularitylocal–nonlocal operatorboundary behavioursingular nonlinearityGreen's function estimates

MSC classification

Primary: 35A01: Existence problems
Secondary: 35R11: Fractional partial differential equations 47G20: Integro-differential operators 35S15: Boundary value problems for pseudodifferential operators 35B65: Smoothness and regularity of solutions 35J75: Singular elliptic equations

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 155 , Issue 1 , February 2025 , pp. 10 - 56
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Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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