Luo Jianzhong's face changed suddenly, of course he understood what the four major journals meant.

In this era, mathematicians who have the strength to publish papers in the four major journals will undoubtedly rank among the top mathematicians in China.

If the qualifications are deeper, they are even eligible to run for the academician of the Academy of Sciences.

You must know that in the entire Lincheng University, let alone academician-level scholars, even second-level senior professors, there is no existence.

Luo Jianzhong himself, in the ranking of domestic mathematicians, is only a first-class position, otherwise he would not be the head of the mathematics department of Lincheng University.

Yesterday, Pang Xuelin's papers have already made Luo Jianxin love talents, if Pang Xuelin can really solve the problem of Zhikov's conjecture, it means that Pang Xuelin has the potential to become an academician.

"No matter what, we have to find a way to keep Mr. Pang at Lincheng University to teach."

Luo Jianzhong secretly made up his mind.

Pang Xuelin didn't know that his words had already caused waves in the Luo Jian Center.

His tone was still steady and unhurried: "The importance of the Laplace equation is well known, and since the 80s of this century, the theory of the Laplace equation has been successfully extended to the p-Laplace equation. Here, the p-LAPLACE operator △pu, i.e., div(|▽u|p-3▽u), where p>1 is a constant. Especially when p=2, △s is Laplace△ in the usual sense. The p(x)-Laplace operator is △p(x)u=div(|▽u|p(x)-3▽u), where p(x) is a real-valued function on the region Ω in the RN. p(x)-Laplace has an important application background in elastic mechanics and other problems, and it reflects the so-called 'point-by-point' physical phenomenon. ”

……

"The variational problem corresponding to the p(x)-Laplace equation involves an integral functional with a p(x)-growth condition. The Russian mathematician Zhikov was the first to study the regularity problem of such integral functionals, and he gave an example to show that such ranges can not be regular, i.e., the Lavrentiev phenomenon can occur. ”

……

Pang Xuelin said as he began to write on the blackboard.

[Let Ω be the open set in RN, p≥1,W^1,p(Ω) and W0^1,p(Ω) represent the standard Sobolev space. Let f:Ω×RN→R satisfy the Caratheodory condition. For a given p∈[1,∞], note: J(p)=inf{∫Ωf(x,△u)dx,u∈W0^1,p(Ω)}. If J(p) is not related to p∈[1,∞], then f is said to be regular, otherwise f is non-regular, or f has a Lavrentiev phenomenon. 】

[We know that when f satisfies the standard p-growth condition, i.e., there is a certain p≥1, such that when (x,ξ) ∈Ω× RN there is: c1|ξ|^p-c0≦|f(x,ξ)|≦c2|ξ|^p+c0, f is always regular, i.e., the Lavrentiev phenomenon does not occur. 】

[However, when f satisfies the p(x)-growth condition, c1(ξ)^p-c0≦|f(x,ξ)|≦c2|ξ|^p+c0, Zhikov's counterexample shows that for some functions p(x), f is not regular, which reflects the complexity of the problem when formulating the p(x)-growth condition.]

……

There was a slight discussion in the audience, of course, these discussions mainly came from a few professors and associate professors who understood what Pang Xuelin was talking about.

For most students and lecturers, the expressions on their faces at this time are in a state of bewilderment.

"No, this Teacher Pang, do you want to deconstruct Zhikov's conjecture at the report meeting?"

"According to Mr. Pang's meaning, how do I feel that Zhikov's conjecture does not seem to be valid."

"Zhikov guesses that if it is not true, how can he publish a paper at the level of a district."

"District 1? I think I can try to submit to the four major journals! ”

"It's really amazing, I didn't expect a rural primary school to hide such a character."

……

Wang Muhui and Zhang Hewen looked at each other.

They didn't understand what Pang Xuelin was talking about, but there was no doubt that judging from the reactions of the professors in the audience, what Pang Xuelin said should be very awesome.

Of course, what really shocked them was not only the unclear formulas and the professors' reactions, but more importantly, the aura that Pang Xuelin presented during the explanation.

It was as if there was no intention of communicating with the scholars in the audience, but giving a lecture to everyone and to those professors.

When she was studying at Fudan, a Nobel laureate from the United States came to Fudan for an exchange, and she was fortunate to attend that lecture.

The feeling that scholar gave her was similar to the feeling that Pang Xuelin gave her today.

But the problem is that the Nobel Prize winner has long been famous all over the world and has equal honors, while Pang Xuelin is just a rural primary school teacher.

Such a huge difference in identity, but showing a similar aura, made Wang Muhui feel a great sense of disobedience.

Zhang Hewen's eyes lit up, as a senior media person, he could clearly feel the extremely high news value of Pang Xuelin, even if he put aside the identity of a rural primary school teacher, a young genius in his early twenties is also very valuable for reporting.

Pang Xuelin didn't care about the reaction of the audience, and continued to write on his board.

[Theorem 1.1 If p(x) is a Holder continuous function on Ω, then f satisfying c1(ξ)^p-c0≦|f(x,ξ)|≦c2|ξ|^p+c0 is regular]

……

Pang Xuelin put down the chalk and said with a smile: "According to the above theorem, we can give the answer to the negative of the Zhikov conjecture!" ”

Therefore, in order to study the p(x)-Laplace equation and its related problems, the original theoretical framework of Sobolev space is no longer applicable. So I systematically established the Lebesgue-Sobolev space in a generalized sense, W^k,p|x|(Ω) related theories, the classical Sobolev embedding theorem and Lions' symmetric tight embedding theorem in space W^k,p|x|(Ω). ”

……

Pang Xuelin's voice continued, but under the podium, it was completely quiet.

Many professors have begun to take out paper and pens to check the conclusions given by Pang Xuelin.

As for the ordinary lecturers and the students who came to join in the fun, they are generally in a state of three questions in life.

Who am I?

Where am I?

What the hell am I doing?

Wang Muhui gently touched the girl next to her with her hand: "Do you understand what Teacher Pang said?" ”

The girl shook her head a little dazedly.

Wang Muhui said in a low voice: "Then you still take it so seriously?" ”

The girl said, "Don't you think Professor Pang's lecture is particularly charming?" ”

"Is there one?"

Wang Muhui looked up at Pang Xuelin.

It seems to be a little.

After talking about the p(x)-Laplace equation and the Zhikov conjecture, Pang Xuelin continued to explain the variational principle and non-smooth analysis.

From time to time, some new theories and concepts that were only available in later generations are interspersed.

It directly makes those scholars who have studied nonlinear functional analysis enjoyable.

They even had a faint feeling that as long as they thoroughly studied what Pang Xuelin said today, they could publish a few papers on the first district on this basis.

Although Luo Jianzhong has little understanding of what Pang Xuelin said because of problems in his research field, he also realizes the value of this report: "Lao Wang, you have picked up a big treasure for our mathematics department this time!" ”

"Yes, I didn't expect that Mr. Pang would have such deep attainments in the field of functional analysis."

Wang Chongqing copied Pang Xuelin's board book and said with emotion.

He is the subject leader in the field of functional analysis in the Department of Mathematics of Lincheng University, and he can better understand the significance of what Pang Xuelin is talking about today.

Wang Chongqing even had a faint feeling that as long as these things were integrated and written into a review in the field of functional analysis, it would completely cause a sensation in the international mathematical community.

The minutes passed, and before I knew it, it was close to nine o'clock in the evening.

Pang Xuelin said with a smile: "Okay, I'll talk about nonlinear functional analysis today. If you have any questions, you can summarize the relevant questions to Professor Wang Chongqing, and I will answer them for you one by one after a while! ”

The words fell, and the applause was thunderous.

This time, both the professors and the students who came to listen to the lecture gave Pang Xuelin a warm applause.

Although the students couldn't understand it, from the reactions of the professors, they could also see how powerful Pang Xuelin's content was today.

"Haha, yesterday there were still people who questioned Mr. Pang's academic level, but I saw it today......

"How do I feel that Mr. Pang is much more powerful than the professors in our school......"

"That's true, those professors were a little arrogant at first, and then they all took out pen and paper to take notes, just like we listen to lectures on a daily basis."

……

One by one, the students walked out of the classroom with great interest.

Pang Xuelin got down from the podium, Luo Jianzhong took the lead in getting up, shook hands with Pang Xuelin and said, "Mr. Pang, you really gave me a big surprise, I didn't expect you to study so deeply in the field of functional analysis, it's really surprising." ”

"Director Luo has won the award, I just repeated some of the things I studied before."

Luo Jianzhong said with a smile: "If you are so humble, you are arrogant, Mr. Pang, tomorrow is the weekend, the school is not working, next Monday, you can come directly to the school to go through the entry procedures of the Institute of Mathematics and Physics, and I can adjust the allowance to 500 yuan per month!" ”

Pang Xuelin was slightly stunned, and said with a light smile: "Director Luo, thank you very much!" ”

Pang Xuelin naturally doesn't like a lot of money, in this world, compared to what he wants to do, this money is far from enough.

Next, Pang Xuelin chatted with several other professors for a while, and then rode out of school with Wang Chongqing's father and daughter.

Along the way, most of the time, Wang Chongqing asked Pang Xuelin about the problems related to nonlinear functional analysis, and Pang Xuelin calmly gave corresponding explanations.

Wang Muhui followed behind the two of them, and wanted to interject and talk to Pang Xuelin several times, but she never found a suitable opportunity.

If before, Wang Muhui was a little strange about why her father's attitude towards Pang Xuelin was so enthusiastic, then now, she faintly understands.

Even herself, after listening to this report, she had a faint feeling of being convinced by Pang Xuelin.

()