The will of Christ
'Not what I will, but what you will' — the will of Christ in the monothelite controversy, condemned at Constantinople III, which appealed to Chalcedon's two-natures definition.
Mark 14:32-42
32They came to a place which was named Gethsemane. He said to his disciples, “Sit here, while I pray.”
33He took with him Peter, James, and John, and began to be greatly troubled and distressed.
34He said to them, “My soul is exceedingly sorrowful, even to death. Stay here, and watch.”
35He went forward a little, and fell on the ground, and prayed that, if it were possible, the hour might pass away from him.
36He said, “Abba, Father, all things are possible to you. Please remove this cup from me. However, not what I desire, but what you desire.”
37He came and found them sleeping, and said to Peter, “Simon, are you sleeping? Couldn’t you watch one hour?
38Watch and pray, that you may not enter into temptation. The spirit indeed is willing, but the flesh is weak.”
39Again he went away, and prayed, saying the same words.
40Again he returned, and found them sleeping, for their eyes were very heavy, and they didn’t know what to answer him.
41He came the third time, and said to them, “Sleep on now, and take your rest. It is enough. The hour has come. Behold, the Son of Man is betrayed into the hands of sinners.
42Arise! Let’s get going. Behold: he who betrays me is at hand.”
What each tradition says
Rabbinic / Midrashic
No sourced position found. Checked The Jewish Encyclopedia: there is no 'Gethsemane' article (alphabetical probe of the G listings), and s.v. 'Jesus of Nazareth' mentions the garden only as where he hid and was betrayed (xiv. 42), with nothing on the prayer or the will of Christ; the two-wills dispute is inner-Christian.
Patristic
Hilary says Jesus' words "Yet not as I will, but as Thou wilt" show that His spontaneous prayer for the cup's removal expresses His fellowship with human anxiety. Yet Jesus also associates Himself with the decree of the Will He shares inseparably with the Father.
Hilary of Poitiers (c. 315-367), De Trinitate (On the Trinity), Book X, in NPNF ser. 2, vol. 9 (trans. S. C. Gayford; Oxford, 1899) — Book X, section 37 (on the Gethsemane prayer)
Catholic
Ambrose, cited by Aquinas, reads Luke 22:42 as distinguishing Christ's will from the Father's: "His will" refers to the Man, while the Father's refers to the Godhead. As Christ assumed my will, He assumed my sorrow. The will of man is temporal, but the will of the Godhead is eternal.
Thomas Aquinas (1225-1274); trans. Fathers of the English Dominican Province (1920), Summa Theologiae, Second and Revised Edition (New Advent) — III, q. 18, a. 1 ('Whether there are two wills in Christ'), sed contra (citing Luke 22:42 with Ambrose)
Orthodox
The council says the two natural wills are not contrary to one another, as the impious heretics assert. Christ's human will follows, not resisting or reluctant, but subject to his divine and omnipotent will; the flesh was moved yet subject to the divine will, according to Athanasius.
The Sixth Ecumenical Council (Constantinople III, 680-681), The Definition of Faith, in The Seven Ecumenical Councils, NPNF ser. 2, vol. 14 (ed. Philip Schaff and Henry Wace, trans. H. R. Percival; Edinburgh, 1900) — Session XVIII (the Definition), on the two natural wills
Reformed / Protestant
Calvin says some imagined that Christ's will was but one and simple. Yet Christ, as he was God, willed nothing different from the Father, and from this it follows that his human soul had affections distinct from the secret purpose of God.
John Calvin (1509-1564), Commentary on a Harmony of the Evangelists, Matthew, Mark, and Luke, vol. 3 (trans. William Pringle; Edinburgh: Calvin Translation Society, 1846) — Harmony on Matthew 26:36-44; Mark 14:32-40; Luke 22:39-46 (on Mark 14:36)
Evangelical
Barnes holds that since Jesus was man as well as God, it is not inconsistent that he was deeply affected by sorrows like a man. When Jesus speaks of his will, he expresses what human nature would desire amid such sufferings: it naturally shrank from them and sought deliverance, yet he sought to do God's will.
Albert Barnes (1798-1870), Notes on the New Testament, Explanatory and Practical (enlarged ed. by Robert Frew; CCEL carries the Baker reprint) — Note on Matthew 26:39 (the parallel of Mark 14:36)