Solvability of elliptic systems with square integrable boundary data

By P. Auscher, A. Axelsson, A. Mcintosh. 2008

110 citations recorded by the source corpus.

We consider second order elliptic divergence form systems with complex measurable coefficients A that are independent of the transversal coordinate, and prove that the set of A for which the boundary value problem with L2 Dirichlet or Neumann data is well posed, is an open set. Furthermore we prove that these boundary value problems are well posed when A is either Hermitean, block or constant. Our methods apply to more general systems of partial differential equations and as an example we prove perturbation results for boundary value problems for differential forms.

Subfields: Applied Mathematics, Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/83e1ede37000e25d16b23570f2623c0ecaeb7375

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In Applied Mathematics

In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Weighted maximal regularity estimates and solvability of non-smooth elliptic systems I (2009, methodology): “As compared to [9], we here use subscript 0 to denote restriction to the boundary R at t = 0, rather than the normal component of f .”
The method of layer potentials in Lp and endpoint spaces for elliptic operators with L∞ coefficients (2013, background): “2 was shown to hold in general, for L and L∗ satisfying the ‘standard assumptions’, in work of Rosén [49], in which L(2)-bounds for layer potentials are obtained via results of [6] concerning functional calculus of certain first-order ‘Dirac-type’ operators.”
Regularity theory for solutions to second order elliptic operators with complex coefficients and the L Dirichlet problem (2016, background): “Finally, there are perturbation results in a variety of special cases, such as [3] and [2]; the first paper shows that solvability in L(2) implies solvability in L for p near 2, and the second paper has L(2)-solvability results for small L∞ perturbations of real elliptic operators when the complex m”
Representation and uniqueness for boundary value elliptic problems via first order systems (2014, methodology): “stant coeﬃcients in arbitrary dimension: IL= ( n n+1 ,∞). This will imply compatible well-posedness of each of the four boundary value problems in every possible class considered here using results in[AAMc]. For general systems, IL is an open interval and contains [ 2n n+2 ,2]. In [HKMP1], it is pro”