Interior regularity of solutions of differential equations

  • Lars Hörmander
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 116)


The simplest case of the results proved in this chapter is the fact that every u Є C 2 satisfying the Laplace equation
$$ % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qacqGHciITpaWaaWbaaSqabeaapeGaaGOmaaaakiaadwhacaGGVaGa % eyOaIyRaamiEa8aadaahaaWcbeqaa8qacaaIYaaaaOGaey4kaSIaey % OaIy7damaaCaaaleqabaWdbiaaikdaaaGccaWG1bGaai4laiabgkGi % 2kaadMhapaWaaWbaaSqabeaapeGaaGOmaaaakiabg2da9iaaicdaaa % a!47EB! {\partial ^2}u/\partial {x^2} + {\partial ^2}u/\partial {y^2} = 0 $$
is actually in C and can even be expanded in a convergent power series in x and y. The literature devoted to results of this kind is very extensive, so we shall only mention here a few papers which are particularly closely related to the results and methods of this chapter.


Differential Operator Constant Coefficient Principal Part Partial Differential Operator Elliptic Differential Equation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1969

Authors and Affiliations

  • Lars Hörmander
    • 1
  1. 1.University of LundSweden

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