scholarly journals Variational inequalities with lack of ellipticity. Part I: Optimal interior regularity and non-degeneracy of the free boundary

2003 ◽  
Vol 52 (2) ◽  
pp. 361-398 ◽  
Author(s):  
Donatella Danielli ◽  
Nicola Garofalo ◽  
Sandro Salsa
Keyword(s):  
Free Boundary ◽  
Variational Inequalities ◽  
Interior Regularity

A free surface problem arising in the drainage of a uniformly irrigated field: Existence and uniqueness results

1984 ◽  
Vol 36 (3) ◽  
pp. 389-403 ◽  
Author(s):  
John Van Der Hoek ◽  
C. J. Barnes ◽  
J. H. Knight
Keyword(s):  
Free Surface ◽  
Free Boundary ◽  
Boundary Value Problem ◽  
Variational Inequalities ◽  
Existence And Uniqueness ◽  
Free Boundary Value Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Tile Drains ◽  
Porous Soil

AbstractA field comprising uniformly porous soil overlying an impervious subsoil is drained through equally spaced tile drains placed on the boundary between the two layers of soil. When this field is subject to uniform irrigation, a free boundary forms in the porous region above the zone of saturation. We study the free boundary value problem which thus arises using the theory of variational inequalities. Existence and uniqueness results are established.

Remarks on the quasi-steady one phase Stefan problem

1986 ◽  
Vol 102 (3-4) ◽  
pp. 263-275 ◽  
Author(s):  
Bento Louro ◽  
José-Francisco Rodrigues
Keyword(s):  
Free Boundary ◽  
Variational Inequalities ◽  
Specific Heat ◽  
Rate Of Convergence ◽  
Stefan Problem ◽  
Free Boundaries ◽  
Variational Solutions ◽  
The One ◽  
Regularity Results ◽  
Boundary Estimates

SynopsisThis paper presents some regularity results on the solution and on the free boundary for the one phase Stefan problem with zero specific heat in the framework of the variational inequalities formulation. In particular we show the Hölder continuity of the free boundary. Estimates on the rate of convergence when the specific heat vanishes are given for the variational solutions and for the free boundaries.

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