Strongly elliptic operators with distributional coefficients

الأصل · EN

We study operators of the form L=∑|α|,|ᵦ|≤ ₙ Dαcα,ᵦ Dβ, xⁿ provided that the coefficients of the main symbol corresponding to the indices |α|=|β|=m are continuous while the other ones are distributions. Assuming that the main symbol defines the strongly elliptic operator we find sufficient conditions for the coefficients cα,ᵦ(x) which guarantee that the operator L is well defined. In particular, if cα,ᵦ(x) belong to the spaces of multipliers from H₂ᵐ⁻|α| to H₂|β|⁻ᵐ then L defines a maximal sectorial operator in L₂(Rⁿ). We also describe the spaces of multipliers.