Displaying similar documents to “On the regularity of weak solutions to nonlinear elliptic systems of partial differential equations [Abstract of thesis]”

Weak compactness of solutions for fourth order elliptic systems with critical growth

Paweł Goldstein, Paweł Strzelecki, Anna Zatorska-Goldstein (2013)

Studia Mathematica

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We consider a class of fourth order elliptic systems which include the Euler-Lagrange equations of biharmonic mappings in dimension 4 and we prove that a weak limit of weak solutions to such systems is again a weak solution to a limit system.

An example of a nonlinear second order elliptic system in three dimension

Josef Daněček, Marek Nikodým (2004)

Commentationes Mathematicae Universitatis Carolinae

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We provide an explicit example of a nonlinear second order elliptic system of two equations in three dimension to compare two C 0 , γ -regularity theories. We show that, for certain range of parameters, the theory developed in (2002), gives a stronger result than the theory introduced in , 1995. In addition, there is a range of parameters where the first theory gives H"older continuity of solution for all γ < 1 , while the theory is not applicable at all. ...