Recovery of an interface from boundary measurement in an elliptic differential equation

2011 ◽  
Vol 36 (2) ◽  
pp. 201-220 ◽  
Author(s):  
Weifu Fang ◽  
Suxing Zeng
Keyword(s):  
Differential Equation ◽  
Elliptic Differential Equation ◽  
Boundary Measurement

scholarly journals Higher Integrability of Weak Solutions to a Class of Double Obstacle Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhenhua Hu ◽  
Shuqing Zhou
Keyword(s):  
Differential Equation ◽  
Weak Solutions ◽  
Second Order ◽  
Obstacle Problems ◽  
Elliptic Differential Equation ◽  
Higher Integrability ◽  
Global Higher Integrability ◽  
Quasilinear Elliptic

We first introduce double obstacle systems associated with the second-order quasilinear elliptic differential equationdiv(A(x,∇u))=div f(x,u), whereA(x,∇u),f(x,u)are twon×Nmatrices satisfying certain conditions presented in the context, then investigate the local and global higher integrability of weak solutions to the double obstacle systems, and finally generalize the results of the double obstacle problems to the double obstacle systems.

Coefficient Jump-Independent Approximation of the Conforming and Nonconforming Finite Element Solutions

2016 ◽  
Vol 8 (5) ◽  
pp. 722-736
Author(s):  
Shangyou Zhang
Keyword(s):  
Differential Equation ◽  
Finite Element ◽  
Elliptic Equations ◽  
Order Approximation ◽  
Elliptic Differential Equation ◽  
Optimal Order ◽  
Nonconforming Finite Element ◽  
Numerical Tests ◽  
Conforming Finite Element ◽  
Theoretical Finding

AbstractA counterexample is constructed. It confirms that the error of conforming finite element solution is proportional to the coefficient jump, when solving interface elliptic equations. The Scott-Zhang operator is applied to a nonconforming finite element. It is shown that the nonconforming finite element provides the optimal order approximation in interpolation, in L2-projection, and in solving elliptic differential equation, independent of the coefficient jump in the elliptic differential equation. Numerical tests confirm the theoretical finding.

scholarly journals Hölder continuity of solutions of some degenerate elliptic differential equations

2000 ◽  
Vol 62 (3) ◽  
pp. 369-377 ◽  
Author(s):  
Ahmed Mohammed
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Weak Solutions ◽  
Function Spaces ◽  
Elliptic Differential Equation ◽  
Holder Continuity ◽  
Hölder Continuous ◽  
Elliptic Differential Equations ◽  
Continuity Of Solutions ◽  
Degenerate Elliptic

Weak solutions of the degenerate elliptic differential equation Lu := −div(A (x)∇u)+b·∇u+Vu = f, with |b|2ω−1, V, f in some appropriate function spaces, will be shown to be Hölder continuous.

scholarly journals Nonlinear definition of the shadowy mode in higher-order scalar-tensor theories

2021 ◽  
Vol 2021 (12) ◽  
pp. 020
Author(s):  
Antonio De Felice ◽  
Shinji Mukohyama ◽  
Kazufumi Takahashi
Keyword(s):  
Differential Equation ◽  
Coordinate System ◽  
Three Dimensional ◽  
Spacelike Hypersurface ◽  
Higher Order ◽  
Elliptic Differential Equation ◽  
Unitary Gauge ◽  
Definition Of

Abstract We study U-DHOST theories, i.e., higher-order scalar-tensor theories which are degenerate only in the unitary gauge and yield an apparently unstable extra mode in a generic coordinate system. We show that the extra mode satisfies a three-dimensional elliptic differential equation on a spacelike hypersurface, and hence it does not propagate. We clarify how to treat this “shadowy” mode at both the linear and the nonlinear levels.

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