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The Existence of Entropy Solutions for an Elliptic Problems Involving Variable Exponent
Journal of Harbin University of Science and Technology, 2022 In order to study the entropy solution of a class of quasilinear elliptic equations with variable exponents, first, the approximation problem of elliptic equations is established under weak operator conditions, and then the Sobolev embedding theorem ...
LU Yue-ming, LIU Yang
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Elliptic Equations with Degenerate Weights [PDF]
SIAM Journal on Mathematical Analysis, 2020 We obtain new local Calderon-Zygmund estimates for elliptic equations with matrix-valued weights for linear as well as non-linear equations. We introduce a novel log-BMO condition on the weight M.
A. Balci +3 more
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Вестник КазНУ. Серия математика, механика, информатика, 2021 The methods of complex analysis constitute the classical direction in the study of elliptic equations and mixed-type equations on the plane and fundamental results have now been obtained. In the early 60s of the last century, a new theoretical-functional
B. D. Koshanov, A. D. Kuntuarova
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Elliptic blowup equations for 6d SCFTs. Part IV. Matters
Journal of High Energy Physics, 2021 Given the recent geometrical classification of 6d (1, 0) SCFTs, a major question is how to compute for this large class their elliptic genera. The latter encode the refined BPS spectrum of the SCFTs, which determines geometric invariants of the ...
Jie Gu +4 more
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A remark on partial data inverse problems for semilinear elliptic equations [PDF]
Proceedings of the American Mathematical Society, 2019 We show that the knowledge of the Dirichlet-to-Neumann map on an arbitrary open portion of the boundary of a domain in $\mathbb{R}^n$, $n\ge 2$, for a class of semilinear elliptic equations, determines the nonlinearity uniquely.
Katya Krupchyk, G. Uhlmann
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Differential-Difference Elliptic Equations with Nonlocal Potentials in Half-Spaces
Mathematics, 2023 We investigate the half-space Dirichlet problem with summable boundary-value functions for an elliptic equation with an arbitrary amount of potentials undergoing translations in arbitrary directions.
Andrey B. Muravnik
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Inverse problems for elliptic equations with power type nonlinearities [PDF]
Journal des Mathématiques Pures et Appliquées, 2019 We introduce a method for solving Calderon type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for certain nonlinear equations in ...
M. Lassas +3 more
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Multiplicity results for $(p,q)$ fractional elliptic equations involving critical nonlinearities [PDF]
Advances in Differential Equations, 2018 In this paper we prove the existence of infinitely many nontrivial solutions for the class of $(p,\, q)$ fractional elliptic equations involving concave-critical nonlinearities in bounded domains in $\mathbb{R}^N$.
M. Bhakta, Debangana Mukherjee
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Regularity of solutions to a class of variable–exponent fully nonlinear elliptic equations [PDF]
Journal of Functional Analysis, 2018 In the present paper, we propose the investigation of variable-exponent, degenerate/singular elliptic equations in non-divergence form. This current endeavor parallels the by now well established theory of functionals satisfying nonstandard growth ...
Anne C. Bronzi +3 more
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Regularity for Fully Nonlinear Elliptic Equations with Oblique Boundary Conditions [PDF]
Archive for Rational Mechanics and Analysis, 2017 In this paper, we obtain a series of regularity results for viscosity solutions of fully nonlinear elliptic equations with oblique derivative boundary conditions. In particular, we derive the pointwise Cα, C1,α and C2,α regularity. As byproducts, we also
Dong-Sheng Li, Kai Zhang
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