Results 21 to 30 of about 110,790 (301)

The Pohozaev-type inequalities and their applications for a kind of elliptic equation (system)

Boundary Value Problems, 2020
In this paper, we first derive a new kind of Pohozaev-type inequalities for p-Laplacian equations in a more general class of non-star-shaped domains, and then we take two examples and their graphs to explain the shape of the new kind of the non-star ...
Bingyu Kou, Tianqing An, Zeyan Wang
doaj   +1 more source

Singularities and regularity of stationary Stokes and Navier-Stokes equations on polygonal domains and their treatments

AIMS Mathematics, 2020
The solution fields of the elliptic boundary value problems may exhibit singularities near the corners, edges, crack tips, and so forth of the physical domain. The corner singularity theory for the solutions of elliptic boundary value problems on domains
Yasir Nadeem Anjam
doaj   +1 more source

Optimal metric regularity in general relativity follows from the RT-equations by elliptic regularity theory in $L^p$ -spaces [PDF]

, 2018
Shock wave solutions of the Einstein equations are constructed in coordinates systems in which the gravitational metric is only Lipschitz continuous, but the connection $\Gamma$ and curvature $Riem(\Gamma)$ are both in $L^{\infty}$, the curvature being ...
Moritz Reintjes, B. Temple
semanticscholar   +1 more source

Existence and regularity of multivalued solutions to elliptic equations and systems [PDF]

Communications in analysis and geometry, 2013
We extend the work of Simon and Wickramasekera, who constructed a large class of $C^{1,\mu}$ multivalued solutions to the minimal surface equation, to produce $C^{1,\mu}$ multivalued solutions to more general classes of elliptic equations and systems ...
B. Krummel
semanticscholar   +1 more source

New elliptic system and global solutions for the constraints equations in General relativity [PDF]

Communications in Mathematical Physics, 1971
By a new choice of the arbitrarily given quantities on an initial 3-manifold we reduce the system of constraints, in General Relativity, to an elliptic system of four equations, the coefficients of which have a simple geometric interpretation on the 3-manifold. The system seems well suited for a global study and some results are given in this direction.
openaire   +2 more sources

Multivalued solutions of multidimensional linear equations of heat conduction and rivertons

Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2021
Background. The article considers the problem of calculating multivalued solutions of multidimensional linear parabolic equations. Solutions for this type of equations of heat conductivity in dimension d > 2 were not previously known and represent an ...
V.M. Zhuravlev, V.M. Morozov
doaj   +1 more source

A universal variational framework for parabolic equations and systems [PDF]

Calculus of Variations and Partial Differential Equations, 2022
We propose a variational approach to solve Cauchy problems for parabolic equations and systems independently of regularity theory for solutions. This produces a universal and conceptually simple construction of fundamental solution operators (also called
P. Auscher, Moritz Egert
semanticscholar   +1 more source

Novel numerical method based on cubic B-splines for a class of nonlinear generalized telegraph equations in irregular domains

Alexandria Engineering Journal, 2020
In this work, a cubic B-spline method based on finite difference and meshless approaches for solving 2D generalized telegraph equations in irregular single and multi-connected domains is presented.
Sergiy Reutskiy, Yuhui Zhang, Ji Lin, Hongguang Sun   +3 more
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Generalized Hitchin Systems and the Knizhnik–zamolodchikov–bernard Equation on Ellipic Curves [PDF]

Letters in Mathematical Physics, 1997
Knizhnik-Zamolodchikov-Bernard (KZB) equation on an elliptic curve with a marked point is derived by the classical Hamiltonian reduction and further quantization. We consider classical Hamiltonian systems on cotangent bundle to the loop group $L(GL(N,{\bf C}))$ extended by the shift operators, to be related to the elliptic module.
openaire   +3 more sources

Systems of quasilinear elliptic equations with dependence on the gradient via subsolution-supersolution method

, 2017
For the homogeneous Dirichlet problem involving a system of equations driven by \begin{document}$(p,q)$\end{document} -Laplacian operators and general gradient dependence we prove the existence of solutions in the ordered rectangle determined by a ...
D. Motreanu, C. Vetro, F. Vetro
semanticscholar   +1 more source