An Application of the Browder-Minty Theorem in a Problem of Partial Differential Equations
2019 ◽
Vol 6
(1)
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pp. 1-12
Keyword(s):
In this work, we will show existence of weak solution for a semilinear elliptic problem using as main tool the Browder-Minty Theorem. First, we will make a brief introduction about basic theory of the Sobolev Spaces to support our study and provide sufficient tools for the development of our work. Then we will take a quick approach on the Browder-Minty Theorem and use this result to show the existence of at least one weak solution to an elliptic Partial Differential Equations (PDE) problem whose nonlinearity, denoted by f, is a known function. For this, in addition to the already mentioned results, we will also use as study tools: Embedding Sobolev Theorems, Linear Continuous Operators Theory, Poincaré Inequality and Hölder Inequality.
Full Stability for a Class of Control Problems of Semilinear Elliptic Partial Differential Equations
2019 ◽
Vol 57
(4)
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pp. 3021-3045
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1996 ◽
Vol 65
(215)
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pp. 943-983
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2015 ◽
Vol 37
(4)
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pp. A1637-A1657
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1999 ◽
Vol 20
(5)
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pp. 1875-1904
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2017 ◽
Vol 33
(6)
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pp. 2005-2022
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1999 ◽
Vol 69
(230)
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pp. 629-653
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2000 ◽
Vol 24
(11)
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pp. 749-751