The Science Fiction World of Xueba

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

In this era, mathematicians who are capable of publishing papers in the four major journals will undoubtedly rank among the top mathematicians in China.

If the qualifications are deeper, you may even be eligible to be an academician of the Chinese Academy of Sciences.

You must know that in the entire Forest City University, let alone academician-level scholars, even the second-level senior professors do not exist.

Luo Jianzhong himself, in the ranking of mathematicians in China, is only at the bottom of the first-class position, otherwise he would not be the head of the Department of Mathematics at Lincheng University.

Yesterday, Pang Xuelin's papers had already made Luo Jianzhong arouse his love for talents. If Pang Xuelin can really solve the Zhikov conjecture problem, it means that Pang Xuelin has the potential to become an academician.

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

Luo Jianzhong secretly made up his mind.

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

His tone was still steady, and he said calmly: "The importance of the equation is well known. Since the 1980s, the theory of the equation has been successfully extended to the p-equation. Here, the p-operator △pu, that is, div(|▽ u|p-3▽u), where p\u003e1 is a constant. Especially when p=2, △s is △ in the usual sense. Here p(x)-operator refers to △p(x)u= div(|▽u|p(x)-3▽u), where p(x) is a real-valued function on the region Ω in RN. p(x)- has important application background in problems such as elastic mechanics, It reflects a physical phenomenon known as 'pointwise anisotropy'."

...

"The variational problem corresponding to the p(x)-equation involves integral functionals with p(x)-growth conditions. The Russian mathematician Zhikov was the first to study the regularity of such integral functionals. He gave an example It shows that such ranges may not be regular, that is, the Lavrentiev phenomenon can occur.”

...

Pang Xuelin started writing on the blackboard while talking.

[Assume Ω is an 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,∞], record: J(p)=inf{∫Ωf(x,△u)dx, u∈W0^1, p(Ω)}. If J(p) has nothing to do with p ∈ [1, ∞], then f is called regular, otherwise f is non-regular, or f has Lavrentiev phenomenon. 】

[We know that when f satisfies the standard p-growth condition, that is, there exists a certain p≥1, so that when (x,ξ)∈Ω×RN: c1|ξ|^p-c0≦|f(x, ξ)|≦c2|ξ|^p+c0, f is always regular, that is, the Lavrentiev phenomenon will 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 with p(x)-growth conditions]

...

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

"No way, this Teacher Pang, is he trying to deconstruct Zhikov's conjecture at the report meeting?"

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

"Zhikov conjectures that if it doesn't hold true, it will be possible to produce a paper at the level of a district."

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

"It's amazing. I didn't expect such a character to be hidden in a rural elementary school."

...

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 was talking about should be very powerful.

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

It was as if, in this report meeting, it seemed that there was no intention to communicate with the scholars in the audience, but to give lectures to everyone and to those professors.

Wang Muhui felt vaguely familiar with this scene. When she was studying at Fudan University, once, a Nobel Prize winner from the United States came to Fudan University for an exchange. She was fortunate to participate in that report meeting.

The feeling that the 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 Pang Xuelin is just a mere rural elementary 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 high news value of Pang Xuelin. Even leaving aside his status as a rural primary school teacher, a young genius in his early twenties is still very newsworthy.

Pang Xuelin didn't care about the audience's reaction and continued writing on the blackboard.

[Theorem 1.1 If p(x) is a Holder continuous function on Ω, then f that satisfies 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 a negative answer to Zhikov's conjecture!"

"Therefore, if you want to study the p(x)-equation and related issues, the original theoretical framework of Sobolev space is no longer applicable. So I systematically established the generalized Lebesgue-Sobolev space W^k, p|x |(Ω) related theory, obtained the natural extension form of the classic Sobolev embedding theorem and the symmetric compact embedding theorem in the space W^k, p|x|(Ω).”

...

Pang Xuelin's voice continued, but the bottom of the podium was completely silent.

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

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

who I am?

Where am I?

What am I doing?

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

The girl shook her head blankly.

Wang Muhui whispered: "Then you still take it so seriously?"

The girl said: "Don't you think Professor Pang's lecture is very charming?"

"Have it?"

Wang Muhui looked up at Pang Xuelin.

It seems to be a bit.

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

Interspersed from time to time are some new theories and concepts that only later generations have.

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

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

Although Luo Jianzhong had a little understanding of what Pang Xuelin said because of problems in the research field, he also realized the value of this report: "Old Wang, you brought back a big treasure for our mathematics department this time. !"

"Yeah, I didn't expect Mr. Pang to have such profound attainments in the field of functional analysis."

Wang Chongqing said with emotion while copying Pang Xuelin's writing on the blackboard.

He is the academic leader in the field of functional analysis of the Department of Mathematics of Lincheng University, and he can better understand the meaning of what Pang Xuelin said today.

Wang Chongqing even has a vague feeling that as long as these things are integrated and written into a review in the field of functional analysis, it can completely cause a sensation in the international mathematics community.

Time passed by every minute and every second, and before you knew it, it was almost nine o'clock in the evening.

Pang Xuelin said with a smile: "Okay, I will stop here first about the content of nonlinear functional analysis today. If you have any questions, you can summarize the relevant questions to Professor Wang Chongqing, and I will explain them one by one after a while. Answer everyone!"

The voice fell, and there was thunderous applause.

This time, both the professors and the students who came to attend the class gave Pang Xuelin warm applause.

Although the students didn't understand, they could tell from the professors' reactions how powerful Pang Xuelin's speech was today.

"Haha, there were still people who questioned Teacher Pang's academic level yesterday, you have seen it today..."

"Why do I feel that Teacher Pang is much better than the professors in our school..."

"It's true. Those professors were a little arrogant at first, but then they all took out pens and paper to take notes, just like we usually listen to lectures."

...

The students walked out of the classroom chatting enthusiastically one by one.

When Pang Xuelin came down from the podium, Luo Jianzhong got up first, shook hands with Pang Xuelin and said, "Mr. Pang, you really gave me a big surprise. I didn't expect that your research in the field of functional analysis is so deep. It's really surprising."

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

Luo Jianzhong said with a smile: "If you are so self-effacing, you will be arrogant. Teacher Pang, tomorrow is the weekend and the school will not work. Next Monday, you can come directly to the school to go through the entry procedures for the Institute of Mathematics and Physics. I can adjust the allowance for you. Up to five hundred yuan a month!"

Pang Xuelin was taken aback for a moment, then smiled lightly and said, "Director Luo, thank you very much!"

Naturally, Pang Xuelin would not dislike too much money. In this world, compared with what he wanted to do, this amount of money was far from enough.

Next, Pang Xuelin chatted with several other professors for a while, and then left the school with Wang Chongqing and his daughter.

Along the way, most of the time, Wang Chongqing asked Pang Xuelin for advice on nonlinear functional analysis, and Pang Xuelin gave corresponding explanations very calmly.

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

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

Even she herself, after listening to this report meeting, felt faintly convinced by Pang Xuelin.

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