Minimal Regularity (minimal + regularity)

Distribution by Scientific Domains


Selected Abstracts


Minimal regularity of the solutions of some transmission problems

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2003
D. Mercier
We consider some transmission problems for the Laplace operator in two-dimensional domains. Our goal is to give minimal regularity of the solutions, better than H1, with or without conditions on the (positive) material constants. Under a monotonicity or quasi-monotonicity condition on the constants (or on the inverses according to the boundary conditions), we study the behaviour of the solution near vertex and near interior nodes and show in each case that the given regularity is sharp. Without condition we prove that the regularity near a corner is of the form H1+,, where , is a given bound depending on the material constants. Numerical examples are presented which confirm the sharpness of our lower bounds. Copyright © 2003 John Wiley & Sons, Ltd. [source]


Minimal regularity of the solution of some boundary value problems of Signorini's type in polygonal domains

MATHEMATISCHE NACHRICHTEN, Issue 6 2005
Denis Mercier
Abstract We study the regularity in Sobolev spaces of the solution of transmission problems in a polygonal domain of the plane, with unilateral boundary conditions of Signorini's type in a part of the boundary and Dirichlet or Neumann boundary conditions on the remainder part. We use a penalization method combined with an appropriated lifting argument to get uniform estimates of the approximated solutions in order to obtain some minimal regularity results for the exact solution. The same method allows us to consider problems with thin obstacles. It can be easily extended to 3D problems. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]


The infinitesimal rigid displacement lemma in Lipschitz co-ordinates and application to shells with minimal regularity

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2004
Sylvia Anicic
Abstract We establish a version of the infinitesimal rigid displacement lemma in curvilinear Lipschitz co-ordinates. We give an application to linearly elastic shells whose midsurface and normal vector are both Lipschitz. Copyright © 2004 John Wiley Sons, Ltd. [source]


Minimal regularity of the solutions of some transmission problems

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2003
D. Mercier
We consider some transmission problems for the Laplace operator in two-dimensional domains. Our goal is to give minimal regularity of the solutions, better than H1, with or without conditions on the (positive) material constants. Under a monotonicity or quasi-monotonicity condition on the constants (or on the inverses according to the boundary conditions), we study the behaviour of the solution near vertex and near interior nodes and show in each case that the given regularity is sharp. Without condition we prove that the regularity near a corner is of the form H1+,, where , is a given bound depending on the material constants. Numerical examples are presented which confirm the sharpness of our lower bounds. Copyright © 2003 John Wiley & Sons, Ltd. [source]


Minimal regularity of the solution of some boundary value problems of Signorini's type in polygonal domains

MATHEMATISCHE NACHRICHTEN, Issue 6 2005
Denis Mercier
Abstract We study the regularity in Sobolev spaces of the solution of transmission problems in a polygonal domain of the plane, with unilateral boundary conditions of Signorini's type in a part of the boundary and Dirichlet or Neumann boundary conditions on the remainder part. We use a penalization method combined with an appropriated lifting argument to get uniform estimates of the approximated solutions in order to obtain some minimal regularity results for the exact solution. The same method allows us to consider problems with thin obstacles. It can be easily extended to 3D problems. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]