Quasi-linear PDEs and forward–backward stochastic differential equations: Weak solutions [PDF]
Journal of Differential Equations, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chunrong Feng, Huaizhong Zhao
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Hölder continuity of weak solutions of p-Laplacian PDEs with VMO coefficients [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 2019 We consider solutions u ∈ W 1 , p ( Ω ; R N ) of the p -Laplacian PDE ∇ ⋅ ( a ( x ) | D u | p − 2 D u ) = 0 , for x ∈ Ω ⊆ R n , where Ω is open and bounded.
Christopher S Goodrich +1 more
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Some Compactness Criteria for Weak Solutions of Time Fractional PDEs [PDF]
SIAM Journal on Mathematical Analysis, 2017 The Aubin-Lions lemma and its variants play crucial roles for the existence of weak solutions of nonlinear evolutionary PDEs. In this paper, we aim to develop some compactness criteria that are analogies of the Aubin--Lions lemma for the existence of ...
Lei Li, Jian‐Guo Liu
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Growth conditions and regularity for weak solutions to nonlinear elliptic pdes
Journal of Mathematical Analysis and Applications, 2020 We describe some aspects of the process/approach to interior regularity of weak solutions to a class of nonlinear elliptic equations in divergence form, as well as of minimizers of integrals of the calculus of variations.
Paolo Marcellini
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The finite element neural network method to simulate two dimensional partial differential equations and perform parameter identification [PDF]
Scientific ReportsNeural networks (NNs) have received growing interest in engineering due to their ability to assimilate high-dimensional data and provide accurate approximations for complex systems.
Mohammed Abda +7 more
doaj +2 more sources
Existence of Weak Solutions to Nonlocal PDEs With a Generalized Definition of Caputo Derivative
Mediterranean Journal of Mathematics, 2023 Some compactness criteria that are analogies of the Aubin–Lions lemma for the existence of weak solutions of nonlinear evolutionary PDEs play crucial roles for the existence of weak solutions to time-fractional PDEs. Based on this fact, in this paper, we consider the existence of weak solutions to a kind of partial differential equations with Caputo ...
Jiaohui Xu +2 more
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Very weak solutions of linear elliptic PDEs with singular data and irregular coefficients [PDF]
Differential Equations & Applications, 2018 In this article it is shown that linear elliptic PDEs admit very weak solutions for rather singular data – like non-integrable right hand sides or singular Neumann boundary conditions – not only in case of continuous coefficients, but even for general ...
J. Merker
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Weak and Measure-valued Solutions to Evolutionary PDEs
Computers & Mathematics with Applications, 1996 Introduction. Scalar Conservation Laws. Young measures and Scalar Conservation Laws. Measure-Valued Solutions and Nonlinear Hyperbolic Equations. Mathematical Theory for a Class of Non-Newtonian Fluids.
J. Málek
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Regularity results for weak solutions of elliptic PDEs below the natural exponent [PDF]
Annali Di Matematica Pura Ed Applicata, 2015 Several results corrected and revised.
David Cruz-Uribe +2 more
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Global Weak Solutions of PDEs for Compressible Media: A Compactness Criterion to Cover New Physical Situations [PDF]
, 2016 This short paper is an introduction of the memoir recently written by the two authors (see Bresch and Jabin, Global existence of weak solutions for compressible Navier–Stokes equations: thermodynamically unstable pressure and anisotropic viscous stress ...
D. Bresch, Pierre-Emmanuel Jabin
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