Gov. Edmund G. Brown demontrated his current delicate relationship with Jimmy Carter when he telephoned the president Oct 12 to inform him he was meeting in Tijuana the next day with Mexico's president Jose Lopez Portillo and intended to propose U.S.-Mexican Cabinet-level discussions to resolve and impase over Mexican natural gas.

President Carter's response was icy. Would the governor please not take any action that could interfere with U.S. policy? Brown shelved his proposal. Nevertheless, after meeting the Mexican president, he left no doubt that he feels Carter's policy toward Mexico is one of malignant neglect.

That typifies Jerry Brown's mixture of contempt and caution in dealing with the president. Brown has solved the political problems that menaced him this year and may well score a substantial reelection victory strengthening his credentials for a 1980 challenge against Carter. Privately, he has little admiration for the president as a man or a public official.

But Brown and his closest advisers are realists who appreciate that Carter will be impregable if he keeps his post-camp David popularity. "Jerry is not about to make a quixotic move that will destroy him," one member of his inner circle told us. Consequently, Brown shields private contempt with public praise and, as in the Mexican episole, avoids direct confrontation.

Caution stems from appreciation of the Carter revival , not self-doubts by Brown Rather, Brown has managed a pol revolt but in generally solving problems of incumbency. Alone among the many Democratic governors elected in the Watergate year of 1974. Brown seems well ahead for relection and conceivably could be the only one of the lot of survive.

That is significantly arttributable to the atrociously inept campaign run by Brown's Republican foe, state Attorney General Evelle Younger. But Brown himself has evolved from merely charismatic candidate to master politican.

Brown's justly famed leap from foe to ardent supporter of tax-slashing propostion 13 climaxed of series of adjustments. They been in early 1977 when Dow Chemical canceled a California plant, triggering a revulsion against the anti-business, anti-growth tone of the Brown administrations.

He then began systematically mending fences on academic growth, big government, law and order, and agriculture. His campaign brochure takes credit for state spending limits and tough sentencing laws. "Jobs are going up, taxes are going down," he tells every rally.

Brown has no time today for liberal doctrine. Addressing the militantly liberal California Democratic Council (CDC) Brown delivered a 15-minute chamber of Commerce booster speech. While the liberals looked on in utter amazement, Brown boasted about the state's rising corporate profits The CDC has no place else to go, and Brown knows it. Brown's faintly disguised contempt for the liberals betrays his cavalier treatment of supporters and nonsupporters alike that is his underlying weakness as a politician. His CDC performance concluded 24 hours of intermittent rudeness, beginning with a testimonial dinner for state AFL-CIO leader John Henning; in a self-congratulatory speech, Brown did not even mention Henning's name. On the next day, he outraged a national meeting of UPI editors by keeping them waiting for an hour and a half.

But the editors who waited were rewarded with a taste of some of the nation's most innovative political thinking. While proposition 13 obviously reacted to inflation and taxation, Brown told them, it also protested "runaway growth" and "very rapid change." It was, he added, a demand "to slow things down" - a quest for stability.

Thus, behind his curre t applause of growth, Brown still believes this is "an era of limits". To sophisticated audiences such as the UPI editors, he talks about low growth being essential to reduced inflation. In private, he contends the government's appetite for regulation has overreached itself and contributes to inflation.

Brown specifically feels Carter blundered in approaching the energy problem with more, not less, regulation. Moreover, he doubts that Carter can fulfill what Brown now talks of as the Democratic Party's historic missions to stop inflation.

Jerry Brown has no doubt that he can fulfill this mission better than Jimmy Carter. Furthermore, the excitement he has generated this fall on the campaign trail has convinced his handlers that there is still the old Brown magic that bested Carter in seven 1976 primaries. Brown's current caution in confronting the president merely connotes respect for Carter's prsent popularity, which shall be measured very carefully from California in the coming weeks.