TITLE

Stability remarks to the obstacle problem forp-Laplacian type equations

AUTHOR(S)
Rodrigues, Jos� Francisco
PUB. DATE
May 2005
SOURCE
Calculus of Variations & Partial Differential Equations;May2005, Vol. 23 Issue 1, p51
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We extend some convergence andL1 stability results for the coincidence set to thep-obstacle problem under natural nondegeneracy conditions and without restrictions onp,. We rely on the localregularity of the solution and, as an application, we show the existence of a solution to the thermal membrane problem, and in a limit nonlocal case also its uniqueness for small data.
ACCESSION #
16902945

 

Related Articles

  • On dynamics of quantum states generated by the Cauchy problem for the Schrödinger equation with degeneration on the half-line. Sakbaev, V. // Journal of Mathematical Sciences;Jun2008, Vol. 151 Issue 1, p2741 

    The paper considers the Cauchy problem for the Schrödinger equation with operator degenerate on the semiaxis and the family of regularized Cauchy problems with uniformly elliptic operators whose solutions approximate the solution of the degenerate problem. The author studies the strong and...

  • Large solutions to the p-Laplacian for large p. García-Melián, Jorge; Rossi, Julio; Lis, José // Calculus of Variations & Partial Differential Equations;Feb2008, Vol. 31 Issue 2, p187 

    In this work we consider the behaviour for large values of p of the unique positive weak solution u p to Δ p u = u q in Ω, u = +∞ on $$\partial\Omega$$ , where q > p − 1. We take q = q( p) and analyze the limit of u p as p → ∞. We find that when q( p)/ p...

  • Applications of Equilibrium Problems to a Class of Noncoercive Variational Inequalities. Chadli, O.; Liu, Z.; Yao, J. C. // Journal of Optimization Theory & Applications;Jan2007, Vol. 132 Issue 1, p89 

    In this paper, we are interested in the existence of solutions for a class of noncoercive variational inequalities involving a p-Laplacian type operator. Our approach is based essentially on equilibrium problems and arguments from recession analysis. Our results are of two types: the first is...

  • Positive solutions for nonlinear Neumann problems with concave and convex terms. Papageorgiou, Nikolaos; Smyrlis, George // Positivity;Jun2012, Vol. 16 Issue 2, p271 

    We consider a nonlinear elliptic Neumann problem driven by the p-Laplacian with a reaction that involves the combined effects of a 'concave' and of a 'convex' terms. The convex term ( p-superlinear term) need not satisfy the Ambrosetti-Rabinowitz condition. Employing variational methods based on...

  • Elliptic operators and Choquet capacities. Solynin, A. Yu. // Journal of Mathematical Sciences;Apr2010, Vol. 166 Issue 2, p210 

    Choquet capacities generated by solutions of certain elliptic partial differential equations are discussed. Bibliography: 11 titles.

  • The mean-value theorem for elliptic operators on stratified sets. Oshchepkova, S.; Penkin, O. // Mathematical Notes;Apr/May2007, Vol. 81 Issue 3/4, p365 

    In this paper, an analog of the mean-value theorem for harmonic functions is proved for an elliptic operator on the stratified set of “stratified” spheres whose radius is sufficiently small. In contrast to the classical case, the statement of the theorem has the form of a special...

  • The infinity Laplacian in infinite dimensions. Gaspari, Thierry // Calculus of Variations & Partial Differential Equations;Nov2004, Vol. 21 Issue 3, p243 

    We study three properties of real-valued functions defined on a Banach space: The absolutely minimizing Lipschitz functions, the viscosity solutions of the infinity Laplacian partial differential equation, and the functions which satisfy comparison with cones. We prove that these notions are...

  • Lipschitz continuity of state functions in some optimal shaping. Brian�on, Tanguy; Hayouni, Mohammed; Pierre, Michel // Calculus of Variations & Partial Differential Equations;May2005, Vol. 23 Issue 1, p13 

    We prove local Lipschitz continuity of the solution to the state equation in two kinds of shape optimization problems with constraint on the volume: the minimal shaping for the Dirichlet energy, with no sign condition on the state function, and the minimal shaping for the first eigenvalue of the...

  • Mathematical treatment of the discharge of a laminar hot gas in a stagnant colder atmosphere. Antontsev, S. N.; Díaz, J. // Journal of Applied Mechanics & Technical Physics;Jul2008, Vol. 49 Issue 4, p681 

    We study the boundary-layer approximation of the classical mathematical model that describes the discharge of a laminar hot gas in a stagnant colder atmosphere of the same gas. We prove the existence and uniqueness of solutions to a nondegenerate problem (without zones of stagnation of gas...

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sign out of this library

Other Topics