A note on boundary point principles for partial differential inequalities of elliptic type
Boundary Value Problems, 2022 In this note we consider boundary point principles for partial differential inequalities of elliptic type. First, we highlight the difference between the conditions required to establish classical strong maximum principles and classical boundary point ...
John Christopher Meyer
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On the loss of maximum principles for higher-order fractional Laplacians
Proceedings of the American Mathematical Society, 2018 We study existence and positivity of solutions to problems involving higher-order fractional Laplacians (−∆)s for any s > 1. In particular, using a suitable variational framework and the nonlocal properties of these operators, we provide an explicit ...
Nicola Abatangelo +2 more
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On the strong maximum principle [PDF]
Proceedings of the American Mathematical Society, 2001 This paper is concerned with the variational problem: \[ \text{minimize }\int_\Omega f(|\nabla u|) \,dx \quad\text{on }u^0+ W_0^{1,1}(\Omega), \tag{1} \] where \(u^0\) is a given function in \(W^{1,1}(\Omega)\) and \(f\) is a nonnegative, extended valued, lower semicontinuous, and convex function on \(\mathbb R\) such that \(f(0)= 0\), and where ...
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Maximum principles for parabolic systems coupled in both first-order and zero-order terms
International Journal of Mathematics and Mathematical Sciences, 1994 Some generalized maximum principles are established for linear second-order parabolic systems in which both first-order and zero-order terms are coupled.
Chiping Zhou
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Maximum Principles and Aleksandrov-Bakelman-Pucci Type Estimates for NonLocal Schrödinger Equations with Exterior Conditions [PDF]
SIAM Journal on Mathematical Analysis, 2017 We consider Dirichlet exterior value problems related to a class of non-local Schr\"odinger operators, whose kinetic terms are given in terms of Bernstein functions of the Laplacian.
A. Biswas, J. Lörinczi
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Enforcing the non-negativity constraint and maximum principles for diffusion with decay on general computational grids [PDF]
, 2010 In this paper, we consider anisotropic diffusion with decay, and the diffusivity coefficient to be a second-order symmetric and positive definite tensor.
Arnold +65 more
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Maximum principles in symplectic homology [PDF]
Israel Journal of Mathematics, 2017 In the setting of symplectic manifolds which are convex at infinity, we use a version of the Aleksandrov maximum principle to derive uniform estimates for Floer solutions that are valid for a wider class of Hamiltonians and almost complex structures than
W. Merry, I. Uljarević
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New maximum principles for linear elliptic equations
, 2006 We prove extensions of the estimates of Aleksandrov and Bakel$'$man for linear elliptic operators in Euclidean space $\Bbb{R}^{\it n}$ to inhomogeneous terms in $L^q$ spaces for $q < n$.
Kuo, Hung-Ju, Trudinger, Neil S.
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A Liouville type theorem for a class of anisotropic equations
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016 In this paper we are dealing with entire solutions of a general class of anisotropic equations. Under some appropriate conditions on the data, we show that the corresponding equations cannot have non-trivial positive solutions bounded from above.
Barbu Luminiţa, Enache Cristian
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Strong maximum principles for fractional elliptic and parabolic problems with mixed boundary conditions [PDF]
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2016 We present some comparison results for solutions to certain non-local elliptic and parabolic problems that involve the fractional Laplacian operator and mixed boundary conditions, given by a zero Dirichlet datum on part of the complementary of the domain
B. Barrios, María Medina
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