Results 11 to 20 of about 110,790 (301)
Distributed Control of Systems Governed by a General Class of Quasilinear Elliptic Equations
Journal of Differential Equations, 1993 Let \(\Omega\) be a bounded open subset of \(\mathbb{R}^ N\) with Lipschitz continuous boundary; let \(a: \Omega\times \mathbb{R}^ N\to \mathbb{R}^ N\), \(a_ 0: \Omega\times\mathbb{R}\to \mathbb{R}\) be two Carathéodory functions, \(C^ 1\) in the second variable, such that \[ \sum_{i,j=1}^ N \partial_{N+i} a_ j (.,\eta) \xi_ i\xi_ j\geq \Lambda_ 1(k+| \
Luis A. Fernández, Eduardo Casas
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Quasilinear elliptic systems in divergence form associated to general nonlinearities
Advances in Nonlinear Analysis, 2018 The paper is concerned with a priori estimates of positive solutions of quasilinear elliptic systems of equations or inequalities in an open set of Ω⊂ℝN{\Omega\subset\mathbb{R}^{N}} associated to general continuous nonlinearities satisfying a local ...
D’Ambrosio Lorenzo, Mitidieri Enzo
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Lipschitz regularity for elliptic equations with random coefficients
Archive for Rational Mechanics and Analysis, 2015 We develop a higher regularity theory for general quasilinear elliptic equations and systems in divergence form with random coefficients. The main result is a large-scale $L^\infty$-type estimate for the gradient of a solution.
Armstrong, Scott N. +1 more
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Adaptive BEM for elliptic PDE systems, part I: abstract framework, for weakly-singular integral equations [PDF]
Applicable Analysis, 2020 In the present work, we consider weakly-singular integral equations arising from linear second-order elliptic PDE systems with constant coefficients, including, e.g. linear elasticity.
G. Gantner, D. Praetorius
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BMO $$\varepsilon $$-regularity results for solutions to Legendre–Hadamard elliptic systems [PDF]
Calculus of Variations and Partial Differential Equations, 2021 We will establish an $$\varepsilon $$ ε -regularity result for weak solutions to Legendre–Hadamard elliptic systems, under the a-priori assumption that the gradient $$\nabla u$$ ∇ u is small in $$\textrm{BMO}.$$ BMO . Focusing on the case
Christopher Irving
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Vestnik of Samara University Natural Science Series, 2020 It is known that the general theory of multidimensional singular integral operators over the entire space Em was constructed by S. G. Mikhlin. It is shown that in the two-dimensional case, if the operator symbol does not turn into zero, then the Fredholm
G. Dzhangibekov, J. M. Оdinabekov
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Constructive proofs for localised radial solutions of semilinear elliptic systems on Rd
Nonlinearity, 2023 Ground state solutions of elliptic problems have been analysed extensively in the theory of partial differential equations, as they represent fundamental spatial patterns in many model equations. While the results for scalar equations, as well as certain
Jan Bouwe van den Berg +2 more
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Chinese Annals of Mathematics. Series B, 2020 In this paper, the authors consider the asymptotic synchronization of a linear dissipative system with multiple feedback dampings. They first show that under the observability of a scalar equation, Kalman’s rank condition is sufficient for the uniqueness
Tatsien Li, B. Rao
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SINET: Ethiopian Journal of Science, 2023 The Dirichlet and Neumann boundary value problems for the linear second-orderscalar elliptic differential equation with variable coefficients in a bounded two-dimensional domain are considered. The right-hand side the PDE belongs to H´1 pΩq or Hr ´1 pΩq,
Markos F. Yimer, Tsegaye G. Ayele
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Fractal and Fractional, 2021 Numerical methods for spectral space-fractional elliptic equations are studied. The boundary value problem is defined in a bounded domain of general geometry, Ω⊂Rd, d∈{1,2,3}. Assuming that the finite difference method (FDM) or the finite element method (
Stanislav Harizanov +4 more
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