Departments, Schools, Centers & InstitutesThis collection provides access to the research, creative, and scholarly activities of Texas State University.https://digital.library.txstate.edu/handle/10877/12021-04-14T02:47:15Z2021-04-14T02:47:15ZBoundary monotonicity formulae and applications to free boundary problems I: The elliptic caseWeiss, Georg S.https://digital.library.txstate.edu/handle/10877/133722021-04-13T17:29:43Z2004-03-29T00:00:00ZBoundary monotonicity formulae and applications to free boundary problems I: The elliptic case
Weiss, Georg S.
We derive a monotonicity formula at boundary points for a class of nonlinear elliptic partial differential equations, including the obstacle problem case, quenching, a free boundary problem with Bernoulli-type free boundary condition as well as the blow-up case. As application model we prove - for Dirichlet boundary data satisfying certain assumptions - the global existence of a classical solution of the free boundary problem with Bernoulli-type free boundary condition in two and three dimensions.
2004-03-29T00:00:00ZReducibility of zero curvature equationsFlores-Espinoza, Rubenhttps://digital.library.txstate.edu/handle/10877/133712021-04-13T17:19:20Z2004-03-24T00:00:00ZReducibility of zero curvature equations
Flores-Espinoza, Ruben
By introducing a natural reducibility definition for zero curvature equations, we give a Floquet representation for such systems and show applications to the reducibility problem for quasiperiodic 2-dimensional linear systems and to fiberwise linear dynamical systems on trivial vector bundles.
2004-03-24T00:00:00ZA note on a degenerate elliptic equation with applications for lakes and seasBresch, DidierLemoine, JeromeGuillen-Gonzalez, Franciscohttps://digital.library.txstate.edu/handle/10877/133702021-04-12T18:13:14Z2004-03-23T00:00:00ZA note on a degenerate elliptic equation with applications for lakes and seas
Bresch, Didier; Lemoine, Jerome; Guillen-Gonzalez, Francisco
In this paper, we give an intermediate regularity result on a degenerate elliptic equation with a weight blowing up on the boundary. This kind of equations is encountoured when modelling some phenomena linked to seas or lakes. We give some examples where such regularity is useful.
2004-03-23T00:00:00ZExistence of trivial and nontrivial solutions of a fourth-order ordinary differential equationGyulov, TihomirTersian, Stepanhttps://digital.library.txstate.edu/handle/10877/133692021-04-12T17:58:45Z2004-03-23T00:00:00ZExistence of trivial and nontrivial solutions of a fourth-order ordinary differential equation
Gyulov, Tihomir; Tersian, Stepan
We study the multiplicity of nontrivial solutions for a semilinear fourth-order ordinary differential equation arising in spatial patterns for bistable systems. In the proof of our results, we use minimization theorems and Brezis-Nirenberg's linking theorem. We obtain also estimates on the minimizers of the corresponding functionals.
2004-03-23T00:00:00Z