Timeline for How to prove surjectivity of biharmonic operator?

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Dec 16, 2020 at 8:41	history	edited	fatemeh sharifi	CC BY-SA 4.0	added 311 characters in body
Dec 15, 2020 at 15:36	comment	added	fatemeh sharifi		Dear Jochen, thanks for your comment. I've added the boundary conditions to the question's post. Since they are all equal to zero, after integration by parts they disappeared. Please note that I used the notation 'bending moment' $M_{x}, M_{y}$ and shear force $Q_{x},Q_{y}$ instead of 'displacement field' $h$, which have second and third order derivative of the displacement field. For more details about the notation, please see the paper with DOI:10.1016/j.apm.2019.04.036. I used integration by parts and showed the symmetry. But regarding the surjectivity I don't have any clue in my mind!
Dec 15, 2020 at 15:23	history	edited	fatemeh sharifi	CC BY-SA 4.0	added 413 characters in body
Dec 15, 2020 at 10:12	comment	added	Jochen Glueck		Crossposted from Mathematics Stack Exchange. Please explicitly mention and link the crosspost within your question in such a case.
Dec 15, 2020 at 9:58	history	edited	Jochen Glueck	CC BY-SA 4.0	Fixed a typoe.
Dec 15, 2020 at 9:57	comment	added	Jochen Glueck		Welcome to MathOverflow! First a remark concerning the symmetry: The domain of your operator is too large, i.e., it does not encode any boundary conditions; this implies that the operator is actually not symmetric (in order to prove symmetry, you need to integrate by parts, and there you need certain $0$-boundary conditions which ensure that the occurring boundary terms vanish).
Dec 15, 2020 at 9:53	history	edited	fatemeh sharifi	CC BY-SA 4.0	deleted 9 characters in body
Dec 15, 2020 at 9:26	review	First posts
Dec 15, 2020 at 9:33
Dec 15, 2020 at 9:20	history	asked	fatemeh sharifi	CC BY-SA 4.0