In the Game of Thrones/ASoIaF universe are the details of Elia Martell's death public knowledge? And if so why did Oberyn take so long to look for revenge?
It is unclear how many of the details are known, but considering the number of people involved it would be inevitable that the Martells learned the gruesome details of their fate.
The Martells themselves were enraged with the murder of Elia and her children. Oberyn wanted to continue the war and champion the cause of Viserys Targaryen, the only surviving Targaryen prince, but Doran Martell, who had succeeded his mother as ruler of Dorne, knew that they were not strong enough and made his peace.
Oberyn's rage actually seems to come from learning the fate of his sister:
Oberyn had a very close relationship with his sister Elia. Following the Sack of King's Landing, when he learned that she was raped and murdered by a Lannister knight, Gregor Clegane, along with her son and how her daughter was killed by another Lannister knight (Amory Lorch), he attempted to raise Dorne for Viserys. The new Hand, Jon Arryn, was able to keep the peace, but Oberyn has desired revenge ever since.
Beware that these links go to wiki pages which contain numerous spoilers WRT the books and possibly the TV show.
From "Tyrion IV" in "A Clash of Kings", it appears there still is an unsolved mystery WRT her death:
“Why forget?” Tyrion smiled. “I’ve promised to deliver his sister’s killers, alive or dead, as he prefers. After the war is done, to be sure.”
Varys gave him a shrewd look. “My little birds tell me that Princess Elia cried a . . . certain name . . . when they came for her.”
“Is a secret still a secret if everyone knows it?” In Casterly Rock, it was common knowledge that Gregor Clegane had killed Elia and her babe. They said he had raped the princess with her son’s blood and brains still on his hands.
“This secret is your lord father’s sworn man.”
On whether it was public knowledge or not, ACOK chapter 53.
“Oberyn knows that Gregor was the one who...” “He knows nothing. He has heard tales. Stable gossip and kitchen calumnies. He has no crumb of proof. Ser Gregor is certainly not about to confess to him. I mean to keep him well away for so long as the Dornishmen are in King’s Landing.” “And when Oberyn demands the justice he’s come for?” “I will tell him that Ser Amory Lorch killed Elia and her children,” Lord Tywin said calmly. “So will you, if he asks.” “Ser Amory Lorch is dead,” Tyrion said flatly. “Precisely. Vargo Hoat had Ser Amory torn apart by a bear after the fall of Harrenhal. That ought to be sufficiently grisly to appease even Oberyn Martell.”
The long game, ADWD chapter 43
The parchment was written in the Common Tongue. The queen unrolled it slowly, studying the seals and signatures. When she saw the name Ser Willem Darry, her heart beat a little faster. She read it over once, and then again. “May we know what it says, Your Grace?” asked Ser Barristan. “It is a secret pact,” Dany said, “made in Braavos when I was just a little girl. Ser Willem Darry signed for us, the man who spirited my brother and myself away from Dragonstone before the Usurper’s men could take us. Prince Oberyn Martell signed for Dorne, with the Sealord of Braavos as witness.” She handed the parchment to Ser Barristan, so he might read it for himself. “The alliance is to be sealed by a marriage, it says. In return for Dorne’s help overthrowing the Usurper, my brother Viserys is to take Prince Doran’s daughter Arianne for his queen.” The old knight read the pact slowly. “If Robert had known of this, he would have smashed Sunspear as he once smashed Pyke, and claimed the heads of Prince Doran and the Red Viper ... and like as not, the head of this Dornish princess too.” “No doubt that was why Prince Doran chose to keep the pact a secret,” suggested Daenerys. “If my brother Viserys had known that he had a Dornish princess waiting for him, he would have crossed to Sunspear as soon as he was old enough to wed.” “And thereby brought Robert’s warhammer down upon himself, and Dorne as well,” said Frog. “My father was content to wait for the day that Prince Viserys found his army.”